What is a partial sum of an infinite series?

A partial sum ${S}_{n}$ of an infinite series ${\sum}_{i = 1}^{\infty} {a}_{i}$ is the sum of the first n terms, that is,
${S}_{n} = {a}_{1} + {a}_{2} + {a}_{3} + \cdots + {a}_{n} = {\sum}_{i = 1}^{n} {a}_{i}$.