Question

Could someone who is good with series explain why the answer to this question is E?

Answer 1

for one thing, the first one does not converge at all, so we can toss that one out

Answer 2

the last one is easy, it is a geometric series with \(r=\frac{1}{2}\) so when you sum it up you get
\[\frac{1}{1-\frac{1}{2}}=2\]

Answer 3

Why does the first one diverge?

Answer 4

because... well because it does

Answer 5

for one thing, the terms do not even go to zero in the limit

Answer 6

\[\lim_{n\to \infty}\frac{2n}{n+3}=2\]
if the terms go not go to zero, there is no way you can add an infinite number of them up and get a finite number

Answer 7

*do not

Answer 8

i bet we can add up the last one as well
do you know how to sum a geometric series?