What would you like to understand?

To determine if an infinite series converges or diverges when given an explicit formula for its $n$-th partial sum $S_n$, evaluate the limit $\lim_{n \to \infty} S_n$. If this limit exists and is a finite value, the series converges to that value; if the limit is infinite or does not exist, the series diverges.

Conditions: You are given an explicit algebraic formula for the $n$-th partial sum, $S_n$.; The limit is taken as $n \to \infty$.

To determine if an infinite series converges or diverges when given an explicit formula for its $n$-th partial sum $S_n$, evaluate the limit $\lim_{n \to \infty} S_n$. If this limit exists and is a finite value, the series converges to that value; if the limit is infinite or does not exist, the series diverges.

Conditions: You are given an explicit algebraic formula for the $n$-th partial sum, $S_n$.; The limit is taken as $n \to \infty$.