What series should I use to compare? Direct comparison test Use direct comparison test to prove if the following series converge or not. 
A) $\sum_{n=0}^\infty \frac{1}{3^n -1}$
B) $\sum_{n=0}^\infty\frac{1}{\sqrt{n+2}}$
In A) I wrote $3^n -1<3^n$ so $\frac{1}{3^n -1}>\frac{1}{3^n}$, but that is useless because $\frac{1}{3^n}$ converges and it's smaller than $\frac{1}{3^n-1}$ so I can't conclude anything. 
And then in B) I don't know what series I should use to compare.

For A) use that $$\frac{1}{3^n-1}<\frac{2}{3^n}$$ this is equivalent to $$2<3^n$$
