I have the following sequence \(\displaystyle (x_{n})\) , \(\displaystyle x_{n}=1+\frac{1}{2^{2}}+...+\frac{1}{n^{2}}\) which has the limit \(\displaystyle \frac{\pi ^{2}}{6}\).I need to calculate the limit of the sequence \(\displaystyle (y_{n})\) , \(\displaystyle y_{n}=1+\frac{1}{3^{2}}+...+\frac{1}{(2n-1)^{2}}\)
I don't know how to start.I think I need to solve the limit for all the sequence ( even n + odd n) then from the "big limit" I should subtract \(\displaystyle \frac{\pi ^{2}}{6}\).How to start?
I don't know how to start.I think I need to solve the limit for all the sequence ( even n + odd n) then from the "big limit" I should subtract \(\displaystyle \frac{\pi ^{2}}{6}\).How to start?