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No.726 ã®æçš¿ãã芧ããã ããã°ã¹ãããªããããšæããŸãã
NEWNo.737DD++3æ23æ¥ 17:41
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NEWNo.738éãããã3æ23æ¥ 18:24
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NEWNo.739éãããã3æ23æ¥ 20:18
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NEWNo.741éãããã3æ23æ¥ 22:12
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NEWNo.742DD++仿¥ 01:42
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500幎é£ç¶ããŠèµ·ããªã確çã¯{1-1/(365x1000)}^(500x365)=60.65%ã§ãã
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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100幎éèµ·ããªã確çã¯ã(1-(1/1000))^100=90.47921%
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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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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No.713DD++3æ21æ¥ 13:23
ïŒããã1,000幎ã«äžåºŠãããªããã§ããã
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No.715DD++3æ21æ¥ 18:25
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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.717ããããã¯ã¡ã¹ã3æ22æ¥ 07:13
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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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6; 3141549
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10; 31415925457
11; 314159264013
12; 3141592649625
13; 31415926532017
14; 314159265350589
15; 3141592653588533
16; 31415926535867961
17; 314159265358987341
18; 3141592653589764829
19; 31415926535897744669
20; 314159265358978759661
21; 3141592653589792630933
22; 31415926535897931085161
23; 314159265358979322639853
24; 3141592653589793234680617
25; 31415926535897932384615349
26; 314159265358979323823745421
27; 3141592653589793238428435569
28; 31415926535897932384568540625
29; 314159265358979323846212602093
30; 3141592653589793238462579472373
31; 31415926535897932384626459376945
32; 314159265358979323846263865968245
33; 3141592653589793238462643289640533
34; 31415926535897932384626432234171745
35; 314159265358979323846264338399627025
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18;
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No.702ããããã¯ã¡ã¹ã3æ18æ¥ 18:29
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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
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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
å³ã¡
lim[n->oo]Î (k=1,n,(2*k)*(2*k+2)/(2*k+1)^2)=Ï/4â
ããã¯ãŸãã¬ã³ã颿°ã䜿ãã°
Î(3/2)^2 ã«ãã£ãŠã瀺ãããã
ããã§â ã3以äžã®çŽ æ°pã«éå®ã«ããŠã¿ãŠkçªç®ã®çŽ æ°ãprime(k)ã§è¡šããš
lim[n->oo]Î (k=2,n,(prime(k)-1)*(prime(k)+1)/prime(k)^2â¡
å³ã¡
=(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
ããã«ãã¯ã¡ã¹ãããããªã€ã©ãŒç©ã¯ééãã§ãããšããŠæ²èŒããŠããçåŒ
[{(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
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No.627GAI3æ12æ¥ 07:44
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No.634GAI3æ12æ¥ 09:38
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No.636ããããã¯ã¡ã¹ã3æ12æ¥ 10:28
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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
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No.643ããããã¯ã¡ã¹ã3æ12æ¥ 20:14
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ãååšããŠãä»»æã®æ£ã®èªç¶æ° n ã«ã€ããŠ
a_n < e < b_n
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No.646Dengan kesaktian Indukmu3æ13æ¥ 09:19
Dengan kesaktian Indukmuæ§ããã¯ããããããŸãã
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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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ãæ¯èŒããŠÏ^2/6=Σ[k=0..â] 1/(k^2)ãçè«ã¥ããŠããŸãããåãåŒãããx^5,x^7ã®é
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ããã§ããªã€ã©ãŒã¯ãΣ[k=0..â] 1/(k^4)ããx^5ã®é
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((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
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S2=1/(1^3*3^3) + 1/(2^3*4^3) + 1/(3^3*5^3) + 1/(4^3*6^3) +
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No.669HP管çè
3æ14æ¥ 20:44 1/(n^3(n+1)^3)=(6n^2-3n+1)/n^3-(6(n+1)^2+3(n+1)+1)/(n+1)^3
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No.670ãããã3æ14æ¥ 23:06
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