I'm working on a series but since the thing that I need help with is only a simple inequality, this seems like the appropriate subsection to post this thread in.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\sum\limits_{n = 1}^\infty {\left( { - 1} \right)^n \frac{{\log \left( n \right)}}{{\sqrt n }}}

[/tex]

With the limits I've pretty much been given, the limit of the terms is zero and the terms are greater than zero for all finite n. I've got a feeling that the series does converge. So I need to show that a_n >= a_(n+1) for all n, or that the inequality holds from a certain point anyway.

[tex]

\frac{{\log \left( n \right)}}{{\sqrt n }} \ge \frac{{\log \left( {n + 1} \right)}}{{\sqrt {n + 1} }}

[/tex]

I can't think of a way to explicitly show the above inequality. I thought about rewriting the argument of the logarithm as square root but that doesn't appear to lead anywhere.

Any help would be great thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Establishing an inequality

**Physics Forums | Science Articles, Homework Help, Discussion**