Question

is the series divergent of convergent using the integral test:

I'll type it below.

Answer 1

\[\sum_{n=1}^{\infty} e ^{1/n}/n ^{2}\]

Answer 2

You need to start by evaluating the integral.

Answer 3

well it looks like its convergent by p-series. but take the improper integral and see if it gives you an answer

Answer 4

I'm sorry my mind is blank right now. What is the derivative of e^(1/n)

Answer 5

\[\int \frac{e^{\frac{1}{n}}}{n^2}dn = -e^{\frac{1}{n}}\]\[\lim_{n \to \infty}-e^{\frac{1}{n}} = -1\]

Answer 6

got it, thank you.