I have got this question from my friend and, u know I have tried a lot on this question. I tried to take $$\ o^2 + e^2 \ as \ (o+e)^2 - 2o\times e$$
I could find $o+e$, but I couldn't find $o\times e$. here the odd terms means the terms having position as $$2z+1$$ from z=0...to n and even terms having position as 2z from z=0 to n
Hint: The even part of a given function $f(x)$ is obtained as $f_e(x)=\frac12(f(x)+f(-x))$; the odd part can then be found as $f_o(x)=f(x)-f_e(x)=\frac12(f(x)-f(-x))$. The values of $o,e$ can then be deduced by evaluating these functions appropriately.