\(\cfrac{\pi^2}{6}=\cfrac{1}{1^2}+\cfrac{1}{2^2}+\cfrac{1}{3^2}+...\)
and
\(\cfrac{\pi^2}{8}=\cfrac{1}{1^2}+\cfrac{1}{3^2}+\cfrac{1}{5^2}+\cfrac{1}{7^2}+...\)
but,
\(\cfrac{\pi^2}{24}=\cfrac{1}{2^2}+\cfrac{1}{4^2}+\cfrac{1}{6^2}+\cfrac{1}{8^2}+...\)
that odd and even numbers do not contribute equally to \(\sum^{\infty}_1{\cfrac{1}{n^2}}\)
\(\cfrac{3}{24}=\cfrac{1}{8}\ne\cfrac{1}{24}\)
Odd number contributes three times more than even numbers.
Why?
