# convergent or divergent

#### spring

does
$$\displaystyle \sum_{n=2}^\infty \dfrac{1}{(lnn)^2}$$
converge or diverge? how?
also, what is the problem with my latex code?

Last edited:

#### Prove It

MHF Helper
does
$$\displaystyle \sum_{n=2}^\infty \dfrac{1}{(lnn)^2}[\math] converge or diverge? how? also, what is the problem with my latex code?$$
$$\displaystyle I believe that this is convergent, due to it being an over-harmonic series... Also, your code should say \frac, not \dfrac$$

#### Failure

does
$$\displaystyle \sum_{n=2}^\infty \dfrac{1}{(\ln n)^2}[\math] converge or diverge? how? also, what is the problem with my latex code?$$
$$\displaystyle This series diverges by the Cauchy condensation test - Wikipedia, the free encyclopedia \(\displaystyle \sum_n 2^n\frac{1}{\ln^2 2^n}=\sum_n \frac{2^n}{n^2\ln 2}=+\infty$$

As regards your LaTeX code: your LaTeX code was ok, but the closing math tag had a backward instead a forward slash. You really do need to use a forward slash in the closing math tag, like this: $$\displaystyle \ldots [{\color{red}/}\text{math}]$$\)

spring

#### spring

pöf!
backward slash of course! thank you for your help dear Failure.
it is a fine way to use cauchy condensation test for this, but i think its divergence is also proven by limit comparison test with $$\displaystyle \sum_n \frac{1}{n}$$ i have just discovered it!

by the way, thank you for your believing dear Prove It %)