Question about Fourier Series

Hi

Can someone explain these two cases

i have a final Fourier series that is:

$\displaystyle f(t) \sim \frac{\pi}{2} + \frac{4}{\pi} \sum_{i=1}^\infty \frac{cos(2n+1)t}{(2n+1)^2}$ which was simplified from $\displaystyle \frac{1}{\pi}[\frac{2}{n^2} - \frac{2(-1)^{n}}{n^2}]$.

when n -> odd $\displaystyle \frac{4}{\pi n^2}$

when n -> even 0

and other one $\displaystyle f(t) \sim \frac{8}{\pi} \sum_{i=1}^\infty \frac{sin(2n-1)t}{(2n-1)}$ which was simplified from $\displaystyle \frac{2}{\pi n}(2-2(-1)^{n})$

when n -> even 0

when n -> odd $\displaystyle \frac{8}{\pi n}$

when do i use (2n+1) to replace n? and when do i use (2n-1) to replace n?

P.S