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)

Re: Calculus: Series Convergence and Divergence

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?

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 $\displaystyle \frac{1}{n^p\log(n)}>\frac{1}{n\log(n)}$