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

• Jul 7th 2010, 10:01 PM
de20
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?(Headbang)
• Jul 7th 2010, 10:09 PM
pickslides
Read the section on "Ratio Test"

Pauls Online Notes : Calculus II - Ratio Test
• Jul 7th 2010, 10:15 PM
de20
ratio test is inconclusive with this case since lim n->inf n^[(3/n+1)-3/n] =1
• Jul 7th 2010, 10:46 PM
roninpro
The series fails the $n$-th term test.

$\lim_{n\to \infty} n^{3/n}=1$
• Jul 7th 2010, 10:47 PM
mr fantastic
Quote:

Originally Posted by de20
should i use the com parsing test?(Headbang)

Since $\displaystyle {\lim_{n \to +\infty} n^{3/n} = 1}$ the series is clearly divergent by the limit test.