Answer:
Step-by-step explanation:
1) In a telescoping series almost every term cancels either with a prior or with the subsequent term. To determine if a Series converges to a finite value or infinite value we need to calculate its partial sum.
2) So let's start with this sum:
[tex]S=1-1+1-1+1...\sum_{n=1}^{\infty}(-1)^{n-1}\\[/tex]
3) Let's sum its partial sum to find out if it converges or diverges, i.e.:
[tex]\\\sum_{n=1}^{N}(-1)^{n-1}=1+0+1+0+1\\n=1 \:S=1\\n=2\:S=1-1=0\\n=3\:S=1-1+1=1\\n=4\:S=1-1+1-1=0\\n=5\:S=1-1+1-1+1=1[/tex]
4) The value for this
[tex]\\\lim_{n\rightarrow \infty}\sum_{n=1}^{N}(-1)^{n-1}=Limit\: Does\: not\:Exist[/tex]
Then this Telescoping Series is divergent, because it does not converge to a finite value.
