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![[Post New]](/templates/default/images/icon_minipost_new.gif) 23 Dec 2007 12:33:09 IST
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Dis is a very easy Jee problem (1991) n most of us can surely do it. Try it! The correct reply will be rated!!! If S1, S2, S3, ...., Sn are sums of infinite geometric series whose first terms are 1, 2, 3, ...., n and whose common ratios are 1/2, 1/3, 1/4, ...., 1/(n+1) respectively, then find the value of S1^2 + S2^2 + S3^2 +.....+S2n-1^2.
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<TABLE CELLSPACING="1" CELLPADDING="1" BORDER="0">
<TR><TD>
<DIV ALIGN="right">Animated Letters</DIV></TD></TR></TABLE>
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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23 Dec 2007 12:44:35 IST
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i don't think goiitians can't solve such an easy question, waiting 4 replies
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<TABLE CELLSPACING="1" CELLPADDING="1" BORDER="0">
<TR><TD>
<DIV ALIGN="right">Animated Letters</DIV></TD></TR></TABLE>
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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23 Dec 2007 12:49:49 IST
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for infinit GP.. Sn = a/1-r so as per condition,, S1= 2 S2= 3/2..... ...Sn= n+1/n So,,it is... sum of (k+1/k)2 ...with k= 1 to 2n - 1
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23 Dec 2007 12:51:52 IST
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The series is 22 + 32 + 42 + ... (2n)2 Add and subtract 1, and then use the sum of squares formula?
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Will nip in at times to solve problems :)
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23 Dec 2007 12:51:54 IST
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ur expression of Sn is wrong. Lemme tell u, Sn=n+1.
now try and give d final expression.
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<TABLE CELLSPACING="1" CELLPADDING="1" BORDER="0">
<TR><TD>
<DIV ALIGN="right">Animated Letters</DIV></TD></TR></TABLE>
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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23 Dec 2007 12:53:07 IST
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@ karthik, can u give the final xpression
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<TABLE CELLSPACING="1" CELLPADDING="1" BORDER="0">
<TR><TD>
<DIV ALIGN="right">Animated Letters</DIV></TD></TR></TABLE>
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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23 Dec 2007 12:53:36 IST
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who's is wrong? Is mine wrong?
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Will nip in at times to solve problems :)
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23 Dec 2007 12:54:47 IST
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Final expression is 2n(2n+1)( 4n+1)/6 - 1
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Will nip in at times to solve problems :)
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23 Dec 2007 12:56:38 IST
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d Sn given by Tarun_bits is wrong, and Karthik , u r close to the corrct answer but ur expression isn't correct
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<TABLE CELLSPACING="1" CELLPADDING="1" BORDER="0">
<TR><TD>
<DIV ALIGN="right">Animated Letters</DIV></TD></TR></TABLE>
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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23 Dec 2007 12:56:59 IST
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[(n+1)(n+2)(2n+3)]/6 - 1
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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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23 Dec 2007 12:59:16 IST
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Hmm... I don't see any mistake in my solution.....S1 = 2, S2 = 3 similiarly, S2n-1 = 2n,
So the sum is 2^2 + 3^2 + ... + (2n)^2...
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Will nip in at times to solve problems :)
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23 Dec 2007 12:59:18 IST
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nope lokesh, i'll tell the corrct answer in 5-10 min, but need more replies
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<TABLE CELLSPACING="1" CELLPADDING="1" BORDER="0">
<TR><TD>
<DIV ALIGN="right">Animated Letters</DIV></TD></TR></TABLE>
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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23 Dec 2007 13:00:29 IST
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actually karthik, d fundamental mistake u r doing is wat i also did, dats y its a cool jee problem
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<TABLE CELLSPACING="1" CELLPADDING="1" BORDER="0">
<TR><TD>
<DIV ALIGN="right">Animated Letters</DIV></TD></TR></TABLE>
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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23 Dec 2007 13:01:35 IST
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ooooopppppppsssssssss....
i solved upto Sn
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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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23 Dec 2007 13:02:10 IST
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