Discrete Fourier series for a sum of deltas
$\sum\limits_{r=-\infty}^{\infty}\delta[n-rN]$ is a periodic Kronecker delta with period $N$, but the sum to get the fourier coefficients only "uses" one period $\sum\limits_{n = 0}^{N-1}$ so you don't have to worry about the periodic extension of $\delta$ and take just $x[n] = \delta[n]$ as your function. This is going to cancel out every exponential in the sum except when $n=0$, so the result will be independent of the particular coefficient and be just $a_k = 1/N$.