For a start, if you are summing a function of n from 1 to infinity then the notation should say not .

If you want to sum over all the odd numbers, then you can either call them 2n–1 and start at n=1, or you can use 2n+1 but then you must start at n=0.

So in those Fourier series, the cosine sum should have the summation and the sine sum should have the summation .