Let $P,Q:\mathbb{R}\to \mathbb{R}$ are polynomials, and $Q(n)\ne 0$ for $n\in \mathbb{N}$ Suppose, that $\mathrm{deg}(P)<\mathrm{deg}(Q)$. Prove, that infinite sum

$\sum _{n=1}^{\mathrm{\infty}}(-1{)}^{n}\frac{P(n)}{Q(n)}$

$\sum _{n=1}^{\mathrm{\infty}}(-1{)}^{n}\frac{P(n)}{Q(n)}$