determine all p and q so that the series is convergent

freshsoclean

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May 9, 2019
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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

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Nov 16, 2013
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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

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Jan 29, 2005
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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

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May 9, 2019
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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
 
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