# Identify the pattern of terms Here is an exam question of the unit infinite series and series of functions. Identify the pattern of terms and determine whether the following series is convergent 1 -1+1/2 -1/2 + 1/3 - 1/3 + 1/4 - 1/4 ...

Identify the pattern of terms
Here is an exam question of the unit infinite series and series of functions.
Identify the pattern of terms and determine whether the following series is convergent
$1-1+\frac{1}{2}-\frac{1}{2}+\frac{1}{3}-\frac{1}{3}+\frac{1}{4}-\frac{1}{4}\cdots$
Am I supposed to find the ${n}^{th}$ term?
Are there any method of finding a simple general term for the series?
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Sanaa Holder
The sum of this series is $0$
For example for $n\ge 3$ the general term is
$\frac{\left(-1{\right)}^{n+1}}{2\left[\frac{n-1}{2}\right]}$
For an even $n$ we have ${S}_{n}=0$, while for an odd $n$ we have ${S}_{n}=\frac{1}{\frac{n+1}{2}}\to 0.$

Darius Nash
The sum of the first n terms of your series is

Therefore, the sum of your series, which is, by definition, the limit of the partial sums, is $0$