This one I'm not sure how to go about. The series is the sum from 1 to infinity of: $\displaystyle n/(ln(n))^n$ Just from looking at it I'm assuming it converges, but how do I prove it?
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Originally Posted by Tbone456 This one I'm not sure how to go about. The series is the sum from 1 to infinity of: $\displaystyle n/(ln(n))^n$ Just from looking at it I'm assuming it converges, but how do I prove it? Try the Root Test if $\displaystyle \lim\sqrt[n]{|a_n|}<1$ then the series converges, find $\displaystyle \lim\sqrt[n]{\frac{n}{\ln^n(n)}}$
Originally Posted by Mathstud28 Try the Root Test if $\displaystyle \lim\sqrt[n]{|a_n|}<1$ then the series converges, find $\displaystyle \lim\sqrt[n]{\frac{n}{\ln^n(n)}}$ Ok, so with some simplification I assume that ends up going to zero since the ln(n) in the denominator goes to infinity. Thanks!
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