Question

use the integral test to show convergence

Answer 1

\[\sum_{n=1}^{\infty} n^3e^(-x)\]

Answer 2

use integration by parts

and you want \[\sum_{n=1}^{\infty} n^3e^{-n}\]

Answer 3

\[\int\limits_{1}^{\infty}x^3e^{-x}dx\]

use integration by part

Answer 4

\[\int\limits_{1}^{\infty}x^3e^(-x)=\lim_{b \rightarrow \infty}\int\limits_{1}^{b} ???\]

Answer 5

\[\int\limits_{1}^{\infty} n^3e^(-x) = \lim_{b \rightarrow \infty} n^3-e^(-x)\]

Answer 6

you need to use integration by parts

Answer 7

is this what you are looking to write

\[\lim_{t\to\infty}\int\limits_{1}^{t}x^3e^{-x}dx\]

Answer 8

yes thats what i wrote but i used b instead of t