Divergence of sum_(n>= 2) 1/(ln^p n) for 1<p<= oo



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Divergence of n 2 1 ln p n for 1 < p

Answer & Explanation



Beginner2022-10-07Added 5 answers

By the integral test for convergence, you may write, for all N 3,
3 N 1 ln p x d x 3 n N 1 ln p n
but, as N
3 N 1 ln p x d x = ln 3 ln N e t t p d t 1 ln N e t d t = N +
showing the divergence of the series n 2 1 ln p n , 1 < p <

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