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!

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- Nov 6th 2012, 04:46 AMkimsanders82Need help with the exact sum of convergent series
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! - Nov 6th 2012, 05:19 AMProve ItRe: Need help with the exact sum of convergent series
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? - Nov 6th 2012, 06:13 AMkimsanders82Re: Need help with the exact sum of convergent series
Is it e^(2/3)?

- Nov 6th 2012, 03:21 PMProve ItRe: Need help with the exact sum of convergent series