convergence/divergence of series

[roxstar1]

could someone please point me in the right direction on this problem?

determine the convergence/divergence of the series

infinity
E 1/[n(ln n)^2]
n=2

 

[soroban]

Hello, roxstar1!

Could someone please point me in the right direction on this problem?

Determine the convergence/divergence of the series; \(\displaystyle \L\;\sum^{\infty}_{n=2}\,\frac{1}{n(\ln n)^2\)

Use the integral test . . .

We have: \(\displaystyle \L\;\int^{\;\;\;\infty}_2\frac{dx}{x(\ln x)^2} \;= \;\int^{\;\;\;\infty}_2\frac{1}{x}\)\(\displaystyle \cdot\left(\ln x\right)^{-2}\,dx\)

and let \(\displaystyle u\,=\,\ln x\)

 

[roxstar1]

Thanks..i didnt think about using that test