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.