How do you do the Alternating Series Test on this series and what is the...

Alternating series:
A series of the form
$\sum _{n=1}^{\mathrm{\infty }}(-1{)}^{n+1}n{a}_n=a_0-a_1+a_2-a_3+...$
where either all $a_n$ are positive or all $a_n$ are negative, is called an alternating series.
The alternating series test then says: if $|a_n|$ decreases monotonically and $\underset{n\to \mathrm{\infty }}{lim}{a}_n=0$ then the alternating series converges.
Moreover, let L denote the sum of the series, then the partial sum
$S_k=\sum _{n=0}^k(-1{)}^n{a}_n$
approximates L with error bounded by the next omitted term:
$|S_k-L|\le |S_k-S_{k+1}|=a_{k+1}$
$a_n=\frac{1}{n+1}$
$a_{n+1}=\frac{1}{n+2}$

Therefore $a_{n+1}<a_n$

So $a_n$ is monotonically decrea $\sin g$

$a_n>0$ for all $n=1,2,3,...$

$n\to \mathrm{\infty }$

$=0$

So the series converges.

Answer is given below (on video)