# Thread: Calculus: Series Convergence and Divergence

1. ## Calculus: Series Convergence and Divergence

Consider the series (from n=2 to infinity) , 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!

3. ## 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?

4. ## Re: Calculus: Series Convergence and Divergence

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 $01$ then $\frac{1}{n^p\log(n)}>\frac{1}{n\log(n)}$