Solution
= Solution
Here $0<\ln2<1$, so $(\ln2)^{-n}$ grows exponentially rather than decaying. The positive terms $a_n=n^3/(\ln2)^n$ do not tend to zero; indeed they tend to $+\infty$. Therefore \b[the series diverges] by the necessary condition that the <terms of a convergent series tend to zero>.
The <ratio test> gives the same conclusion: $a_{n+1}/a_n=((n+1)/n)^3/\ln2\to1/\ln2>1$.