# determine all p and q so that the series is convergent

#### freshsoclean

##### New member
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

##### Full Member
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

##### Elite Member
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

##### New member
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