Question

∑∞n=1(e1/n)/n diverge or converge? ∑∞n=1(e1/n)/n diverge or converge? @Mathematics

Answer 1

find using comparison test

Answer 2

Can you write this out again. You're taking the sum from n = 1 to infinity of what?

Answer 3

e^1/n over n

Answer 4

So you want to know if
\[ \sum_{i=1}^{\infty} \frac{e^{1/n}}{n} \]
converges?

Answer 5

yes with period from comparison test

Answer 6

Right. Now does \[ \sum_1^\infty 1/n \]
converge?

Answer 7

no its harmonic I think

Answer 8

That's right, it doesn't.

Now if you can show that
\[ \frac{e^{1/n}}{n} > \frac{1}{n} \]
you'll have your result.