# Calculus: Series Convergence and Divergence

• Feb 23rd 2013, 12:32 PM
mathmann
Calculus: Series Convergence and Divergence
Consider the series (from n=2 to infinity) http://www3.wolframalpha.com/Calcula...s=33&w=62&h=39 , p>= 0

A) show the series converges for p > 1
B) determine if the series converges for p=1
C) Show the series diverges for 0<= p< 1

Thanks for the help! (Rofl)
• Feb 23rd 2013, 12:59 PM
emakarov
Re: Calculus: Series Convergence and Divergence
• Feb 23rd 2013, 01:07 PM
mathmann
Re: Calculus: Series Convergence and Divergence
Thanks! I understand that for parts A and B, but for part C would it be a test for divergence? and what test would that be?
• Feb 23rd 2013, 01:25 PM
Plato
Re: Calculus: Series Convergence and Divergence
Quote:

Originally Posted by mathmann
Thanks! I understand that for parts A and B, but for part C would it be a test for divergence? and what test would that be?

If $\displaystyle 0<p<1~\&~n>1$ then $\displaystyle \frac{1}{n^p\log(n)}>\frac{1}{n\log(n)}$