# Poly and logarithms

Calculus Level 4

$\sum_{n=1}^\infty \dfrac1{3^n} , \quad \sum_{n=1}^\infty \dfrac n{3^n} , \quad \sum_{n=1}^\infty \dfrac{n^2} {3^n} , \quad \sum_{n=1}^\infty \dfrac{n^3}{3^n}$

Using method of differences, one can prove that none of the above series is an integer.

Is it also true that $\displaystyle \sum_{n=1}^\infty \dfrac{n^4}{3^n}$ is not an integer?

×