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If 1/1^2 +1/2^2 +1/3^2 +.....upto infinite =pie^2/6 ,then find

If 1/1^2 +1/2^2 +1/3^2 +.....upto infinite =pie^2/6 ,then find

Grade:12th

1 Answers

Arun
25750 Points
6 years ago
Dear Samresh
 
Your question is not complete.
I think your question is-
 
If 1/1^2 + 1/2^2 + 1/3^2 + ........ upto infinity = pi^/6, then 1/1^2 + 1/3^2 + 1/5^2 +..... =
 
Solution
 
 
write the question like this, divide in odd terms n even terms
 
1/1^2 +1/3^2 + 1/5^2.......upto infinity   +  1/2^2 +1/4^2 +1/6^2.......upto infinity = pi/6
 Now from the even terms take common 1/2^2
 
1/1^2 +1/3^2 +1/5^2........    + 1/2^2  ( 1/1^2 + 1/3^2 + 1/5^2+................) =pi/6 
 
now let 1/1^2 + 1/3^2 + 1/5^2..........    =K
 
so we can write 
K +1/2^2(K) = pi/6
K +K/4 = pi/6
5*K/4= pi/6
K=2*pi/15
So
1/1^2 + 1/3^2 + 1/5^2.................. = 2*pi/15
 
Regards
Arun (askIITians forum expert)

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