determine all p and q so that the series is convergent

[freshsoclean]

summation i=2 to infinity (1/n^p((ln(n))^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

 

[Romsek]

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

 

[pka]

summation i=2 to infinity (1/n^p((ln(n))^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

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

 

[freshsoclean]

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

yes i meant n