Questions tagged [telescoping-series]

Let $a,b,c$ be integers such that $a\neq 0$ and $$ a n^2 + b n + c \neq 0 $$ for all positive integers $n$. (a) Prove that if there exists a positive integer $k$ such that $$ b^2 - 4ac = k^2 a^2, $$ then $$ \sum_{n=1}^\infty \frac{1}{a n^2 + b n +…