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===================================================================
\| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
===================================================================
0| 1 | a | a+1 | 2a+1 |3a+2 |5a+3 |8a+5 |3a+8 |a+3 |4a+1 |
--------------------------------------------------------------------ã
10| 5a+4 |9a+5 | 4a+9 | 3a+4 |7a+3 | 7 |7a |7a+7 |4a+7 | a+4 |
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20| 5a+1 |6a+5 | a+6 | 7a+1 |8a+7 |5a+8 |3a+5 |8a+3 | a+8 |9a+1 |
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30| 9 |9a | 9a+9 | 8a+9 |7a+8 |5a+7 |2a+5 |7a+2 |9a+7 |6a+9 |
--------------------------------------------------------------------ã
40| 5a+6 |a+5 | 6a+1 | 7a+6 |3a+7 | 3 |3a |3a+3 |6a+3 |9a+6 |
--------------------------------------------------------------------ã
50| 5a+9 |4a+5 | 9a+4 | 3a+9 |2a+3 |5a+2 |7a+5 |2a+7 |9a+2 | a+9 |
--------------------------------------------------------------------
60| 1 | a | a+1 | 2a+1
ããã
===================================================================
\| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
===================================================================
0| b | a | a+ b| 2a+ b|3a+2b|5a+3b|8a+5b|3a+8b|a+3b |4a+ b |
--------------------------------------------------------------------ã
10| 5a+4b|9a+5b| 4a+9b| 3a+4b|7a+3b| 7b|7a |7a+7b|4a+7b| a+4b |
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20| 5a+ b|6a+5b| a+6b| 7a+ b|8a+7b|5a+8b|3a+5b|8a+3b| a+8b|9a+ b |
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30| 9b|9a | 9a+9b| 8a+9b|7a+8b|5a+7b|2a+5b|7a+2b|9a+7b|6a+9b |
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40| 5a+6b|a+5b | 6a+ b| 7a+6b|3a+7b| 3b|3a |3a+3b|6a+3b|9a+6b |
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50| 5a+9b|4a+5b| 9a+4b| 3a+9b|2a+3b|5a+2b|7a+5b|2a+7b|9a+2b| a+9b |
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60| b| a | a+ b| 2a+ b
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\| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
======================================================================
0| 11| a | a+11| 2a+11|3a+22 |5a+33 |8a+55 |13a+88 |21a+43|24a+31 |
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10|45a+74|69a+5 |14a+79|83a+84|97a+63|80a+47|77a+10|57a+57|34a+67|91a+24 |
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20|25a+91|16a+15|41a+6 |57a+21|98a+27|55a+48|53a+75| 8a+23|61a+98|69a+21 |
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30|30a+19|29a+40|59a+59|88a+99|47a+58|35a+57|82a+15|17a+72|99a+87|16a+59 |
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270| 59|9a+60| 9a+19| 8a+79|7a+98|5a+77|2a+75|7a+52|9a+27|6a+79 |
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280| 5a+6 |a+85 | 6a+91| 7a+76|3a+67| 43|3a+10|3a+53|6a+63|9a+16 |
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290| 5a+79|4a+95| 9a+74| 3a+69|2a+43|5a+12|7a+55|2a+67|9a+22| a+89 |
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300| 11| a | a+11| 2a+11|3a+22|5a+33
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\| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
======================================================================
0| 11| a | a+11| 2a+11|3a+22 |5a+33 |8a+55 |13a+88 |21a+43|34a+31 |
--------------------------------------------------------------------ã
10|55a+74|89a+5 |44a+79|33a+84|77a+63|10a+47|87a+10|97a+57|84a+67|81a+24 |
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20|65a+91|46a+15|11a+6 |57a+21|68a+27|25a+48|93a+75|18a+23|11a+98|29a+21 |
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30|40a+19|69a+40| 9a+59|78a+99|87a+58|65a+57|52a+15|17a+72|69a+87|86a+59 |
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40|55a+46|41a+5 |96a+51|37a+56|33a+7 |70a+63| 3a+70|73a+33|76a+3 |49a+36 |
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50|25a+39| 4a+75|69a+14|73a+89|42a+3 |15a+92|57a+95|72a+87|29a+82| a+69 |
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60|30a+51|31a+20|61a+71|92a+91|53a+62|45a+53|98a+15|43a+68|41a+83 |94a+51 |
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70|35a+34|29a+85|64a+19|93a+4 |57a+23|50a+27| 7a+50|57a+77|64a+27|21a+4 |
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80|85a+31| 6a+35|91a+66|97a+1 |88a+67|85a+68|73a+35|58a+ 3|31a+38 |89a+41 |
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90|20a+79| 9a+20|29a+99|38a+19|67a+18| 5a+37|72a+55|77a+92|49a+47|26a+39 |
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100|75a+86| a+25|76a+11|77a+36|53a+47|30a+83|83a+30|13a+13|96a+43| 9a+56 |
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110| 5a+99|14a+55|19a+54|33a+9 |52a+63|85a+72|37a+35|22a+7 |59a+42|81a+49 |
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120|40a+91|21a+40|61a+31|82a+71|43a+2 |25a+73|68a+75|93a+48|61a+23 |54a+71 |
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130|15a+94|69a+65|84a+59|53a+24|37a+83|90a+7 |27a+90|17a+97|44a+87|61a+84 |
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140| 5a+71|66a+55|71a+26|37a+81| 8a+7 |45a+88|53a+95|98a+83|51a+78|49a+61 |
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150| 39|49a+0 |49a+39|98a+39|47a+78|45a+17|92a+95|37a+12|29a+7 |66a+19 |
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160|95a+26|61a+45|56a+71|17a+16|73a+87|90a+3 |63a+90|53a+93|16a+83|89a+76 |
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170|85a+59|54a+35|39a+94|93a+29|32a+23|25a+52|57a+75|82a+27|39a+2 |21a+29 |
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180|60a+31|81a+60|41a+91|22a+51|63a+42|85a+93|48a+35|33a+28|81a+63|14a+91|
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190|95a+54| 9a+45| 4a+99|13a+44|17a+43|30a+87|47a+30|77a+17|24a+47| a+64 |
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200|25a+11|26a+75|51a+86|77a+61|28a+47| 5a+8 |33a+55|38a+63|71a+18| 9a+81 |
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210|80a+99|89a+80|69a+79|58a+59|27a+38|85a+97|12a+35|97a+32| 9a+67| 6a+99 |
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220|15a+66|21a+65|36a+31|57a+96|93a+27|50a+23|43a+50|93a+73|36a+23|29a+96 |
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230|65a+19|94a+15|59a+34|53a+49|12a+83|65a+32|77a+15|42a+47|19a+62|61a+9 |
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240|80a+71|41a+80|21a+51|62a+31|83a+82|45a+13|28a+95|73a+8 | a+3 |74a+11 |
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250|75a+14|49a+25|24a+39|73a+64|97a+3 |70a+67|67a+70|37a+37| 4a+7 |41a+44 |
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260|45a+51|86a+95|31a+46|17a+41|48a+87|65a+28|13a+15|78a+43|91a+58|69a+1 |
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270|60a+59|29a+60|89a+19|18a+79| 7a+98|25a+77|32a+75|57a+52|89a+27|46a+79 |
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280|35a+6 |81a+85|16a+91|97a+76|13a+67|10a+43|23a+10|33a+53|56a+63|89a+16 |
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290|45a+79|34a+95|79a+74|13a+69|92a+43| 5a+12|97a+55| 2a+67|99a+22| a+89 |
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300| 11|a | a+11| 2a+11|3a+22|5a+33
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b[61] = b[1]*F[59] + b[2]*F[60] ã®äžã®äœã b[1] ã«äžèŽãã
b[62] = b[1]*F[60] + b[2]*F[61] ã®äžã®äœã b[2] ã«äžèŽããããšã«ãããŸãã
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p=-ac/(a^2+b^2)+b
q=-bc/(a^2+b^2)-a
r=-ac/(a^2+b^2)-b
s=-bc/(a^2+b^2)+a
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(a,b) â (0,0) ãã a^2+b^2 â 0
ãã£ãŠã( -ac/(a^2+b^2) + tb , -bc/(a^2+b^2) - ta ) ãšãã座æšã§è¡šãããç¹ã¯ä»»æã®å®æ° t ã«ã€ããŠçŽç· ax + by + c = 0 äžã«ããã
éã«çŽç· ax + by + c = 0 äžã«ããä»»æã®ç¹ã®åº§æšã¯ããã宿° t ãçšã㊠( -ac/(a^2+b^2) + tb , -bc/(a^2+b^2) - ta ) ãšæžããã
ãããã£ãŠãç¹ (X,Y) ãšçŽç· ax + by + c = 0 ãšã®è·é¢ã¯ãç¹ (X,Y) ãšç¹ ( -ac/(a^2+b^2) + tb , -bc/(a^2+b^2) - ta ) ã®è·é¢ã t ã®é¢æ°ãšèãããšãã®æå°å€ãšããŠæ±ããããã
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-ac/(a^2+b^2) + tb - X
= { -ac + b(a^2+b^2)t - a^2*X - b^2*X + abY - abY } / (a^2+b^2)
= { b( (a^2+b^2)t - bX + aY ) - a( aX + bY + c ) } / (a^2+b^2)
-bc/(a^2+b^2) - ta - Y
= { -bc - a(a^2+b^2)t - a^2*Y - b^2*Y + abX - abX } / (a^2+b^2)
= { -a( (a^2+b^2)t - bX + aY ) - b( aX + bY + c ) } / (a^2+b^2)
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= (a^2+b^2){ (a^2+b^2)t - bX + aY )^2 + ( aX + bY + c )^2 } / (a^2+b^2)^2
= { (a^2+b^2)t - bX + aY )^2 + ( aX + bY + c )^2 } / (a^2+b^2)
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ãã㯠t = ( bX - aY ) / (a^2+b^2) ã®ãšãã«æå°å€ ( aX + bY + c )^2 / (a^2+b^2) ããšãã
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d = | aX + bY + c | / â(a^2+b^2)
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No.746éãããã3æ25æ¥ 02:47
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No.747DD++3æ25æ¥ 03:12
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700幎é£ç¶ããŠèµ·ããªã確çã¯{1-1/(365x1000)}^(700x365)=49.658%ã§ãã
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No.708Dengan kesaktian Indukmu3æ19æ¥ 17:18
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3æ19æ¥ 20:11 Dengan kesaktian IndukmuããŸãHP管çè
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500幎éèµ·ããªã確çã¯ã(1-(1/1000))^500=60.637984%
700幎éèµ·ããªã確çã¯ã(1-(1/1000))^700=49.6411%
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700幎éã§èµ·ãã確çãpã§1000幎éã§èµ·ãã確çã¯1ãããæ®ã300幎éã§èµ·ãã確çã¯1-pã§ãã
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No.710ããããã¯ã¡ã¹ã3æ19æ¥ 22:39
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1000 幎以å
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No.711DD++3æ19æ¥ 23:38
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No.712ããããã¯ã¡ã¹ã3æ21æ¥ 07:18
> ããã1,000幎ã«äžåºŠãããªããã§ããã
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1000 幎éã« k åçºçãã確çã P[k] ãšããŠã
1000 幎éã®çºçåæ°ã®æåŸ
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1*P[1] + 2*P[2] + 3*P[3] + âŠâŠ = 1
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P[1] + P[2] + P[3] + âŠâŠ = 1/e
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No.713DD++3æ21æ¥ 13:23
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No.715DD++3æ21æ¥ 18:25
DD++æ§ããã¯ããããããŸãã
700幎起ããªã確çã¯
%i1) float((1-(1/1000))^700);
(%o1) 0.4964114134310993
800幎起ããªã確çã¯
(%i2) float((1-(1/1000))^800);
(%o2) 0.4491491486100754
900幎起ããªã確çã¯
(%i3) float((1-(1/1000))^900);
(%o3) 0.4063866225452045
1000幎起ããªã確çã¯
(%i4) float((1-(1/1000))^1000);
(%o4) 0.367695424770964
2000幎起ããªã確çã¯
(%i7) float((1-(1/1000))^2000);
(%o7) 0.1351999253974996
3000幎起ããªã確çã¯
(%i8) float((1-(1/1000))^3000);
(%o8) 0.0497123939980363
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No.719éãããã3æ22æ¥ 09:20
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No.720DD++3æ22æ¥ 09:21
DD++æ§ãããã«ã¡ã¯ã
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(%i1) float((1-(1/1000))^700);
(%o1) 0.4964114134310993
3000幎起ããªã確çã¯ã
(%i2) float((1-(1/1000))^3000);
(%o2) 0.0497123939980363
10000幎起ããªã確çã¯ã
(%i3) float((1-(1/1000))^10000);
(%o3) 4.517334597704865E-5
50000幎起ããªã確çã¯ã
(%i4) float((1-(1/1000))^50000);
(%o4) 1.88109746912366E-22
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No.722ããããã¯ã¡ã¹ã3æ22æ¥ 12:19
> 1000幎ã«äžåºŠã¯èµ·ãã
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P(1) + P(2) = 0.75
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(x-1/2)^2+y^2=5^(k-1)/4
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2;
(0,0)
(1,0)
4;
(0,±1)
(1,±1)
6;
(-2,0)
(-1,±2)
(2,±2)
(3,0)
8;
(-5,±1)
(-2,±5)
(3,±5)
(6,±1)
10;
(-12,0)
(-7,±10)
(-3,±12)
(4,±12)
(8,±10)
(13,0)
12;
(-27,±5)
(-20,±19)
(-12,±25)
(13,±25)
(21,±19)
(28,±5)
14;
(-62,0)
(-58,±22)
(-37,±50)
(-17,±60)
(18,±60)
(38,±50)
(59,±22)
(63,0)
16;
(-137,±25)
(-102,±95)
(-62,±125)
(-14,±139)
(15,±139)
(63,±125)
(103,±95)
(138,±25)
18;
(-312,0)
(-292,±110)
(-263,±168)
(-187,±250)
(-87,±300)
(88,±300)
(188,±250)
(264,±168)
(293,±110)
(313,0)
20;
(-687,±125)
(-599,±359)
(-512,±475)
(-312,±625)
(-72,±695)
(73,±695)
(313,±625)
(513,±475)
(600,±359)
(688,±125)

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1;
(0,0)
3;
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(2,0)
5;
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(-2,±8)
(7,±5)
7;
(-33,±25)
(12,±40)
(15,±39)
(42,0)
9;
(-208,0)
(-73,±195)
(-58,±200)
(167,±125)
(176,±112)
11;
(-878,±560)
(-833,±625)
(292,±1000)
(367,±975)
(1039,±79)
(1042,0)
13;
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(-5193,±395)
(-1833,±4875)
(-1458,±5000)
(3918,±3432)
(4167,±3125)
(4392,±2800)
15;
(-21958,±14000)
(-20833,±15625)
(-19588,±17160)
(5375,±25481)
(7292,±25000)
(9167,±24375)
(25967,±1975)
(26042,0)
17;
(-130208,0)
(-129833,±9875)
(-54944,±118048)
(-45833,±121875)
(-36458,±125000)
(-26873,±127405)
(97942,±85800)
(104167,±78125)
(109792,±70000)
19;
(-573921,±307359)
(-548958,±350000)
(-520833,±390625)
(-489708,±429000)
(134367,±637025)
(182292,±625000)
(229167,±609375)
(274722,±590240)
(649167,±49375)
(651042,0)

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[1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360]
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(2*2*4*4*6*6*8*8*10*10*12*12*14*14*16*16*18*18*)/(1*1*3*3*5*5*7*7*9*9*11*11*13*13*15*15*17*17*)
=Ï/2
ãšããçåŒããããŸãããã
ããã§ãããã
2*(2*4)/(3*3)*(4*6)/(5*5)*(6*8)/(7*7)*(8*10)/(9*9)*(10*12)/(11*11)*(12*14)/(13*13)*(14*16)/(15*15)*(16*18)/(17*17)*=Ï/2
ãã£ãŠ
(2*4)/(3*3)*(4*6)/(5*5)*(6*8)/(7*7)*(8*10)/(9*9)*(10*12)/(11*11)*(12*14)/(13*13)*(14*16)/(15*15)*(16*18)/(17*17)*=Ï/4
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lim[n->oo]Î (k=1,n,(2*k)*(2*k+2)/(2*k+1)^2)=Ï/4â
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lim[n->oo]Î (k=2,n,(prime(k)-1)*(prime(k)+1)/prime(k)^2â¡
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=(2*4)/(3*3)*(4*6)/(5*5)*(6*8)/(7*7)*(10*12)/(11*11)*(12*14)/(13*13)*(16*18)/(17*17)*
ãã©ããªæ¥µéå€ããšãã®ãã¯é¢çœãããŒããšãªããŸããã
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[{(2+1)(2-1)/2^2}{(3+1)(3-1)/3^2}{(5+1)(5-1)/5^2}{(7+1)(7-1)/7^2}{(11+1)(11-1)/11^2}ã»ã»ã»]*ζ(2)=1
ãå©çšãããŠããããš
3/4*{(2*4)/(3*3)*(4*6)/(5*5)*(6*8)/(7*7)*(10*12)/(11*11)*(12*14)/(13*13)*(16*18)/(17*17)*}*ζ(2)=1
å³ã¡â¡=4/3*(1/ζ(2))
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(8*10)/(9*9)*(14*16)/(15*15)*(20*22)/(21*21)*(24*26)/(25*25)*(26*28)/(27*27)*â¢
ã¯ã©ããªæ¥µéå€ãªã®ããšããããšãèããããã
ããã«ã¯â ,â¡ã®çµæãã
â¢=â /â¡=(Ï/4)/(8/Ï^2)=Ï^3/32
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No.627GAI3æ12æ¥ 07:44
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No.634GAI3æ12æ¥ 09:38
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No.640Dengan kesaktian Indukmu3æ12æ¥ 17:58
Dengan kesaktian Indukmuæ§ãããã°ãã¯ã
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(((((a+b)+c)+d)+e)+f)+ã»ã»ã»
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No.641ããããã¯ã¡ã¹ã3æ12æ¥ 18:43
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No.642Dengan kesaktian Indukmu3æ12æ¥ 19:00
仿¥ã®BSããžãã¬ãªã¬ãªXã¯ã¢ã¬ã«ã®ãŒã®è©±ã§ããã
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No.643ããããã¯ã¡ã¹ã3æ12æ¥ 20:14
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å調å¢å æçæ°å a_n
å調æžå°æçæ°å b_n
ãååšããŠãä»»æã®æ£ã®èªç¶æ° n ã«ã€ããŠ
a_n < e < b_n
ãšãªãããã€
n â â ã®ãšãã«
b_n - a_n â 0
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No.646Dengan kesaktian Indukmu3æ13æ¥ 09:19
Dengan kesaktian Indukmuæ§ããã¯ããããããŸãã
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ãã€ãã¢æ°ã¯ãlimïŒïŒïŒ1/n)^nã§ããnâç¡é倧ã§ããããéäžãã0ã®ç¡éåã«ã§ããŸããããããã£ãŠãæéåã«ã§ãããæçæ°ã«ãªãæ ¹æ ããããŸããã
ãªã€ã©ãŒã¯ãããã埮åã§èšŒæããŠããŸãã
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äž¡æ¹ãšããç¡çæ°ã§ãã
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å調å¢å æçæ°å a_n
å調æžå°æçæ°å b_n
ãååšããŠãä»»æã®æ£ã®èªç¶æ° n ã«ã€ããŠ
a_n < e < b_n
ãšãªãããã€
n â â ã®ãšãã«
b_n - a_n â 0
ãšããããšãã§ããããã§ãã
ãããããå°ã詳ããæããŠããããªãã§ããããïŒ
No.648ããããã¯ã¡ã¹ã3æ13æ¥ 10:27
dengan ãããããŠããã®ã¯ã
e = Σ[k=0..â] 1/(k!)
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No.649DD++3æ13æ¥ 11:02
ïŒdengan ãããããŠããã®ã¯ã
e = Σ[k=0..â] 1/(k!)
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ããã¯ã埮åç©ååŠã®åºæ¬çãªé¢æ°ã䜿ã£ãå®çŸ©ã§ãããã
ç§ã¯ã埮ç©ååŠã䜿ããªããªã€ã©ãŒã®ããŒãŒã«åé¡ã«ã€ããŠèšã£ãŠããŸãã
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ãæ¯èŒããŠÏ^2/6=Σ[k=0..â] 1/(k^2)ãçè«ã¥ããŠããŸãããåãåŒãããx^5,x^7ã®é
ã¯æ±ããããšã¯ã§ããŸãããç§ãèšç®ããŠã§ããŸããã§ããã
ããã§ããªã€ã©ãŒã¯ãΣ[k=0..â] 1/(k^4)ããx^5ã®é
ãæ±ããŠããã¯ãã§ãã
ãªã€ã©ãŒã®åŸ®ç©ååŠã䜿ã£ãŠãx^3ã®é
ãæ¯èŒããŠÏ^2/6=Σ[k=0..â] 1/(k^2)ãçè«ã¥ãã¯ããã®å Žãã®ããšæã£ãŠããŸãã
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1Ïãã7ÏãŸã§ã®æãç®ãèšç®ããŠã¿ãŸããã
((1-x^2/(1Ï)^2) (1-x^2/(2Ï)^2) (1-x^2/(3Ï)^2) (1-x^2/(4Ï)^2) (1-x^2/(5Ï)^2) (1-x^2/(6Ï)^2) (1-x^2/(7Ï)^2))
=x^14ã®é
ãã»ã»ã»x^8ã®é
ã
x^6ã®é
- x^2/(4Ï)^2 x^2/(6Ï)^2 x^2/(7Ï)^2 - x^2/(5Ï)^2 x^2/(6Ï)^2 x^2/(7Ï)^2
- x^2/(4Ï)^2 x^2/(5Ï)^2 x^2/(7Ï)^2 - x^2/(3Ï)^2 x^2/(5Ï)^2 x^2/(7Ï)^2
- x^2/(3Ï)^2 x^2/(4Ï)^2 x^2/(7Ï)^2 - x^2/(4Ï)^2 x^2/(5Ï)^2 x^2/(6Ï)^2
- x^2/(3Ï)^2 x^2/(6Ï)^2 x^2/(7Ï)^2 - x^2/(2Ï)^2 x^2/(6Ï)^2 x^2/(7Ï)^2
- x^2/(1Ï)^2 x^2/(6Ï)^2 x^2/(7Ï)^2 - x^2/(2Ï)^2 x^2/(5Ï)^2 x^2/(7Ï)^2
- x^2/(1Ï)^2 x^2/(5Ï)^2 x^2/(7Ï)^2 - x^2/(3Ï)^2 x^2/(5Ï)^2 x^2/(6Ï)^2
- x^2/(2Ï)^2 x^2/(4Ï)^2 x^2/(7Ï)^2 - x^2/(1Ï)^2 x^2/(4Ï)^2 x^2/(7Ï)^2
- x^2/(2Ï)^2 x^2/(3Ï)^2 x^2/(7Ï)^2 - x^2/(1Ï)^2 x^2/(3Ï)^2 x^2/(7Ï)^2
- x^2/(1Ï)^2 x^2/(2Ï)^2 x^2/(7Ï)^2 - x^2/(2Ï)^2 x^2/(3Ï)^2 x^2/(6Ï)^2
- x^2/(2Ï)^2 x^2/(5Ï)^2 x^2/(6Ï)^2 - x^2/(1Ï)^2 x^2/(5Ï)^2 x^2/(6Ï)^2
- x^2/(3Ï)^2 x^2/(4Ï)^2 x^2/(6Ï)^2 - x^2/(2Ï)^2 x^2/(4Ï)^2 x^2/(6Ï)^2
- x^2/(1Ï)^2 x^2/(4Ï)^2 x^2/(6Ï)^2 - x^2/(1Ï)^2 x^2/(3Ï)^2 x^2/(6Ï)^2
- x^2/(1Ï)^2 x^2/(2Ï)^2 x^2/(6Ï)^2 - x^2/(3Ï)^2 x^2/(4Ï)^2 x^2/(5Ï)^2
- x^2/(2Ï)^2 x^2/(4Ï)^2 x^2/(5Ï)^2 - x^2/(1Ï)^2 x^2/(4Ï)^2 x^2/(5Ï)^2
- x^2/(2Ï)^2 x^2/(3Ï)^2 x^2/(5Ï)^2 - x^2/(1Ï)^2 x^2/(3Ï)^2 x^2/(5Ï)^2
- x^2/(1Ï)^2 x^2/(2Ï)^2 x^2/(5Ï)^2 - x^2/(2Ï)^2 x^2/(3Ï)^2 x^2/(4Ï)^2
- x^2/(1Ï)^2 x^2/(3Ï)^2 x^2/(4Ï)^2 - x^2/(1Ï)^2 x^2/(2Ï)^2 x^2/(4Ï)^2
- x^2/(1Ï)^2 x^2/(2Ï)^2 x^2/(3Ï)^2
x^4ã®é
+ x^2/(6Ï)^2 x^2/(7Ï)^2 + x^2/(5Ï)^2 x^2/(7Ï)^2 + x^2/(4Ï)^2 x^2/(7Ï)^2
+ x^2/(3Ï)^2 x^2/(7Ï)^2 + x^2/(2Ï)^2 x^2/(7Ï)^2 + x^2/(1Ï)^2 x^2/(7Ï)^2
+ x^2/(5Ï)^2 x^2/(6Ï)^2 + x^2/(4Ï)^2 x^2/(6Ï)^2 + x^2/(3Ï)^2 x^2/(6Ï)^2
+ x^2/(2Ï)^2 x^2/(6Ï)^2 + x^2/(1Ï)^2 x^2/(6Ï)^2 + x^2/(4Ï)^2 x^2/(5Ï)^2
+ x^2/(3Ï)^2 x^2/(5Ï)^2 + x^2/(2Ï)^2 x^2/(5Ï)^2 + x^2/(1Ï)^2 x^2/(5Ï)^2
+ x^2/(3Ï)^2 x^2/(4Ï)^2 + x^2/(2Ï)^2 x^2/(4Ï)^2 + x^2/(1Ï)^2 x^2/(4Ï)^2
+ x^2/(2Ï)^2 x^2/(3Ï)^2 + x^2/(1Ï)^2 x^2/(3Ï)^2 + x^2/(1Ï)^2 x^2/(2Ï)^2
x^2ã®é
- x^2/(7Ï)^2 - x^2/(6Ï)^2 - x^2/(5Ï)^2 - x^2/(4Ï)^2 - x^2/(3Ï)^2 - x^2/(2Ï)^2 - x^2/(1Ï)^2
宿°é
+ 1
x^2(å®éã¯x^3)ã®é
ãã
(x^2/Ï^2){1/1^2+1/2^2+1/3^2+1/4^2+1/5^2+1/6^2+1/7^2}=(x^2/Ï^2) Σ1/n^2ã¯ã§ããŸããã
x=4,6(å®éã¯x^5,7)ã®é
ããã§ããŸããããã¡ãªã¿ã«ãx^4ïŒå®éã¯x^5)ã®é
ã¯ããªã€ã©ãŒã«ãããšÏ^4/90ã ããã§ãã
ã€ãŸããåãåŒããæ±ããããŸããã
ããã§ããªã€ã©ãŒã¯ãΣ[k=0..â] 1/(k^4)ããx^5ã®é
ãæ±ããŠããã¯ãã§ãã
No.651ããããã¯ã¡ã¹ã3æ13æ¥ 11:22
ã¯ã¡ã¹ããããžã
a_n = (1 +1/n)^n
b_n = (1 +1/n)^(n +1)
ãšããããã
No.654Dengan kesaktian Indukmu3æ13æ¥ 12:59
Dengan kesaktian Indukmuæ§ãããã«ã¡ã¯ã
a_n = (1 +1/n)^n
b_n = (1 +1/n)^(n +1)
ã§ãnââãšãªããšãa_n=eã«ãªããŸããã
a_nã®ã°ã©ãã¯ãhttp://y-daisan.private.coocan.jp/html/20230313_BMP/2023-3-13-010.png
b_nã®ã°ã©ãã¯ãhttp://y-daisan.private.coocan.jp/html/20230313_BMP/2023-3-13-011.png
b_n-a_nã®ã°ã©ãã¯ãhttp://y-daisan.private.coocan.jp/html/20230313_BMP/2023-3-13-012.pngãšhttp://y-daisan.private.coocan.jp/html/20230313_BMP/2023-3-13-013.png
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