Question

How to show if this converges or diverges?? Please Help

\[\sum_{k=2}^{\infty}\frac{ 4+k^2 }{ e^2k }\]

Answer 1

Is it \[\sum_{k=2}^\infty\frac{4+k^2}{e^2k}\] or \[\sum_{=k2}^\infty\frac{4+k^2}{e^{2k}}\]? In the first case, the general term goes to \[\infty\] when \[k\rightarrow\infty\] so the series diverges.

In the second case, the general term is equivalent to \[\frac{k^2}{e^{2k}}\] which is \[o(e^{-k})\] so the series converges.

Answer 2

so that's

\(\sum_{k=2}^{\infty}\frac{ 4}{ e^2k } + \frac{ k }{ e^2 }\)

???