Please help with the following:
Find the exact sum of the following convergent series:
sum from n=0 to infinity of (2^{n}/(3^{n}n!))
Thanks!
You should know that $\displaystyle \displaystyle \begin{align*} e^x = \sum_{n = 0}^{\infty} \frac{x^n}{n!} \end{align*}$.
Notice that $\displaystyle \displaystyle \begin{align*} \frac{2^n}{3^n \, n!} = \frac{2^n}{3^n} \cdot \frac{1}{n!} = \left( \frac{2}{3} \right)^n \cdot \frac{1}{n!} = \frac{\left( \frac{2}{3} \right)^n }{n!} \end{align*}$.
What do you think your sum has to equal?