The series defined by the sum from n=1 to n=infinity of 1/[n^(1+1/n)] diverges. Although the general term approaches 0 and resembles a p-series with p>1, for large n, the series behaves similarly to 1/n, which is known to diverge. A limit comparison test with the harmonic series, ∑(1/n), confirms this divergence.
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It isn't a ##p## series but, as you say, it's "like" a ##p## series with ##p=1## as ##n## gets large. So if I were you, I would try a limit comparison test with ##\sum\frac 1 n## and see.CourtneyS said:Homework Statement
Does sum from n=1 to n=infinity of 1/[n^(1+1/n)]
converge or diverge.
Homework Equations
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The Attempt at a Solution
The general term goes to 0 and its a p-series with p>1, but for large n the series becomes 1/n pretty much so, even tho p>1 is it divergent?