If 1/1^2 +1/2^2 +1/3^2 +.....upto infinite =pie^2/6 ,then find
Samresh kumar , 7 Years ago
Grade 12th
Algebra> If 1/1^2 +1/2^2 +1/3^2 +.....upto infinit...
1 Answers
Arun
Last Activity: 7 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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