Can anyone tell me why the Fourier series coefficient of $$p(t) = \sum_{n=-\inf}^{\inf}\delta(t-nT)$$ is 1/T? $$\\$$ My derivation shows that it should be$$a_k=1/T \int_{0}^{T}p(t)e^{-j2\pi kt/T}dt\\ = 1/T \int_{0}^{T}{\sum_{n=-\inf}^{\inf}\delta(t-nT)}e^{-j2\pi kt/T}dt\\=1/T\sum_{n=-\inf}^{\inf}\int_{0}^{T}\delta(t-nT)e^{-j2\pi kt/T}dt\\=1/T\sum_{n=-\inf}^{\inf}e^{-j2\pi knT/T}\\=1/T\sum_{n=-\inf}^{\inf}1$$.
Therefore, how come $a_K$ is 1/T?