Question

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

Answer 1

`\displaystyle\sum_(n\ge0)((\ln3)^n)/(n!)=e^(\ln3)=3`

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


`e^x=\displaystyle\sum_(n\ge0)(x^n)/(n!)`

and taking
`x=\ln3`.