# Thread: how to you show the series sigma n^(3/n) converge or diverge?

1. ## how to you show the series sigma n^(3/n) converge or diverge?

How to you show the series sigma n^(3/n) converge or diverge?

Should i use the com parsing test?

2. Read the section on "Ratio Test"

Pauls Online Notes : Calculus II - Ratio Test

3. ratio test is inconclusive with this case since lim n->inf n^[(3/n+1)-3/n] =1

4. The series fails the $n$-th term test.

$\lim_{n\to \infty} n^{3/n}=1$

5. Originally Posted by de20
should i use the com parsing test?
Since $\displaystyle {\lim_{n \to +\infty} n^{3/n} = 1}$ the series is clearly divergent by the limit test.