Find the sum of the series For any integer $n$ define $k(n) = \frac{n^7}{7} + \frac{n^3}{3} + \frac{11n}{21} + 1$ and $$f(n) = 0 \text{if $k(n)$ is an integer ; $\frac{1}{n^2}$ if $k(n)$ is not an integer } $$
Find $\sum_{n = - \infty}^{\infty} f(n)$.
I do not know how to solve such problem of series. So I could not try anything. 
Thank you for your help.

HINT:
Using Fermat's Little theorem, $$n^p-n\equiv0\pmod p$$  where $p$ is any prime and $n$ is any integer
$\displaystyle\implies n^7-n\equiv0\pmod 7\implies \frac{n^7-n}7$ is an integer
Show that $k(n)$ is integer for all integer $n$
