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?
by
Pi Han Goh