#### freshsoclean

##### New member

- Joined
- May 9, 2019

- Messages
- 2

need help trying to figure this out with proof plz? i know the summation from i=2 to infinity of 1/n^p converges for p>1 and diverges for p<1

- Thread starter freshsoclean
- Start date

- Joined
- May 9, 2019

- Messages
- 2

need help trying to figure this out with proof plz? i know the summation from i=2 to infinity of 1/n^p converges for p>1 and diverges for p<1

- Joined
- Jan 29, 2005

- Messages
- 9,757

The question is clearly about the convergence of \(\displaystyle \sum\limits_{n = 2}^\infty {\frac{1}{{{n^p}{{\left[ {\log (n)} \right]}^q}}}} \)

need help trying to figure this out with proof plz? i know the summation from i=2 to infinity of 1/n^p converges for p>1 and diverges for p<1

Do you know that if \(\displaystyle q>0\) then \(\displaystyle \sum\limits_{n = 2}^\infty {{\left[ {\log (n)} \right]}^{-q}}\) diverges ?

Now you need to show some of your own work.

- Joined
- May 9, 2019

- Messages
- 2

yes i meant nWhat you've written can't be what you meant. This is a series over i but i does not appear in the summands.