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![[Post New]](/templates/default/images/icon_minipost_new.gif) 20 Dec 2007 22:06:38 IST
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Given tat 1/12 + 1/22 + 1/32 + 1/42 + ....... =  2 / 6 & 1/12 + 1/32 + 1/52 + ....... = 2 / 8 find de value of [ 0] [ 1] log [(1+x ) / (1-x) ] dx/x
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20 Dec 2007 22:16:30 IST
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is d ans (pi)^2/4
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20 Dec 2007 22:30:45 IST
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log(1+x/1-x) = log(1+x)-log(1-x) =(x-x2/2+x3/3-x^4/4 + ....) - (-x-x^2/2-x^3/3-x^4/4-.... infinity) =2(x+x^3/3 + x^5/5 + .... upto infinity) [ ] [ ] log(1+x/1-x) dx/x = [0 ][ 1] 2(1+x^2/3+x^4/5 + ....) =2 2/8 = 2/4 |
<TABLE CELLSPACING="1" CELLPADDING="1" BORDER="0">
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I am only one,
But still I am one.
I cannot do everything,
But still I can do something;
And because I cannot do everything
I will not refuse to do the something that I can do.
- Edward Everett Hale
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20 Dec 2007 22:42:12 IST
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yup................rahul's answer is perfect.....
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my future signature:
LOKESH SARDANA,
department of Production and Industrial engineering,
Indian Institute of Technology,Roorkee.
Happiness can be found, even in the darkest of times, if one only remembers to turn on the light.
Albus Dumbledore
Harry Potter and the Prisoner of Azkaban movie
There are only two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle.
-- Albert Einstein
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20 Dec 2007 22:53:47 IST
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Thanx a lot Rahul i got it nw if v change de ques to [ 0][ 1] log ( 1- x ) dx/x does de ans cums out to b 2/ 6 juss wanna chk ma ans
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20 Dec 2007 23:09:39 IST
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well in dat case goin d same way
ans vl be -(sum of two series)
=-(pi)^2/6-(pi)^2/8
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<TABLE CELLSPACING="1" CELLPADDING="1" BORDER="0">
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I am only one,
But still I am one.
I cannot do everything,
But still I can do something;
And because I cannot do everything
I will not refuse to do the something that I can do.
- Edward Everett Hale
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20 Dec 2007 23:11:30 IST
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nup............................
answer will - (pi)^2/6
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my future signature:
LOKESH SARDANA,
department of Production and Industrial engineering,
Indian Institute of Technology,Roorkee.
Happiness can be found, even in the darkest of times, if one only remembers to turn on the light.
Albus Dumbledore
Harry Potter and the Prisoner of Azkaban movie
There are only two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle.
-- Albert Einstein
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21 Dec 2007 00:08:06 IST
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yep rite 4gt to tak tat -ve sign it is cumin out to b - 2 / 6 thanx guys fr helpin me out !!
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