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#### Alexmahone

##### Active member

- Jan 26, 2012

- 268

Test for convergence: $\sum_2^\infty\frac{1}{n(\ln n)^p}$ when $p<0$.

Consider the function $f(x)=\frac{1}{x(\ln x)^p}=\frac{(\ln x)^q}{x}$ when $q=-p>0$.

In order to use the integral test, I have to establish that $f(x)$ is decreasing for $x\ge 2$. How do I proceed?

__My working:__Consider the function $f(x)=\frac{1}{x(\ln x)^p}=\frac{(\ln x)^q}{x}$ when $q=-p>0$.

In order to use the integral test, I have to establish that $f(x)$ is decreasing for $x\ge 2$. How do I proceed?

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