Answer
See below.
Work Step by Step
Given a sequence of numbers $\{a_{n}\}$, an expression of the form
$\displaystyle \sum_{n=1}^{\infty}a_{n}=a_{1}+a_{2}+a_{3}+\cdots+a_{n}+\cdots$
is an infinite series.
The number $a_{n}$ is the $n^{th}$ term of the series.
The n-th partial sum of the series is an element of the sequence
$s_{n}=\displaystyle \sum_{k=1}^{n}a_{k}=a_{1}+a_{2}+a_{3}++a_{n}$
If the sequence of partial sums $\{s_{n}\} $ has a limit $L$, then we say that the series converges to the sum $L$ and we write
$\displaystyle \sum_{n=1}^{\infty}a_{n}=L$.
If the sequence of partial sums of the series does not converge, we say that the series diverges.
Example of a convergent series
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{2^{n}}=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\quad=1$
Example of a divergent series:
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n}=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}$
