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Hey, Can I please get the solution for the question attached to the image. :( Thank you.

Hey,
Can I please get the solution for the question attached to the image. :( 
 
Thank you.

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1 Answers

Alfaz Khan
44 Points
8 years ago
∑ 1/(2n-1)² 
you would be adding up 1/n^2 for all of the odd n. If you were to add up 1/n^2 for all of the even n, then the sum would be 
∑1/(2n)^2 
This second sum, however, is easy to compute. We simply factor out the coefficient: 
∑1/(2n)^2 = 
∑1/(2^2*n^2) = 
1/(2^2)*∑1/n^2 = 
1/4*π^2/6 = 
π^2/24 

From there, we can find the sum of the odd terms by noting that 
∑(1/n^2) = ∑1/(2n)^2 + ∑1/(2n - 1)^2 
which means that 
∑1/(2n - 1)^2 = ∑1/n^2 - ∑1/(2n - 1)^2 
= π^2/6 - π^2/24 
= π^2/8 

ANSWER: π^2/8

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