Algebra> If 1/1^2 + 1/2^2 + 1/3^2 + ........ upto ...

If 1/1^2 + 1/2^2 + 1/3^2 + ........ upto infinity = pi^/6, then 1/1^2 + 1/3^2 + 1/5^2 +..... =

Swarnim Bahdauria , 11 Years ago

Grade 11

2 Answers

rajat Bansal

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

1/1^2 + 1/3^2 + 1/5^2.................. = 2*pi/15

Last Activity: 11 Years ago

Rishi Sharma

Dear Student,
Please find below the solution to your problem.

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

Thanks and Regards

Last Activity: 5 Years ago