Question

What is the sum of the series 1 + ln3 + (ln3)^2/2!?

Answer 1

$\displaystyle\sum_{n\ge0}\frac{(\ln3)^n}{n!}=e^{\ln3}=3$

which follows from the power series representation for $e^x$,

$e^x=\displaystyle\sum_{n\ge0}\frac{x^n}{n!}$

and taking $x=\ln3$.