 # 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 ... IJzerboor07 2022-09-13 Answered
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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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 ${S}_{n}=\frac{1}{\frac{n+1}{2}}\to 0.$

We have step-by-step solutions for your answer! 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 $0$

We have step-by-step solutions for your answer!