I am trying to determine whether the following statement is true or false.
Let $a_n$ be an unbounded, non decreasing sequence s.t. $\sum 1/\log(a_n)$ converges.
Then the series $\sum \frac{2^n}{a_n}$ conerverges.
I tried to prove the statement using the comparison test, and I get the expression $\frac{2^n \log(a_n)}{a_n}$.
Im not so sure how to go further with the calculations.
Any hints will be very appreciated.