# What is a convergent infinite series?

An infinite series ${\sum}_{i = 1}^{\infty} {a}_{i}$ is said to be convergent if ${\lim}_{n \to \infty} {S}_{n}$ exists, where ${S}_{n} = {a}_{1} + {a}_{2} + {a}_{3} + \cdots + {a}_{n}$.