Question

Determine whether the given sequence converges, and find its limit if does converge.
{(-1)^n e^n/n!}

Answer 1

the sequence, right, not the series

Answer 2

should be pretty clear that this limit is zero, if you write out what you have exactly

Answer 3

\[\frac{e^n}{n!}\] say take \(n=10\) you get
\[\frac{e}{1}\times \frac{e}{2}\times \frac{e}{3}\times \frac{e}{4}\times \frac{e}{5}\times \frac{e}{6}\times \frac{e}{7}\times \frac{e}{8}\times \frac{e}{9}\times \frac{e}{10}\]

Answer 4

\[\frac{e^6}{6!}<1\] so
\[\frac{e^n}{n!}<\frac{e}{n}\] if \(n>6\)

Answer 5

if lim x^n/n! =0 then it converges. Thanks for the help!