# Math Help - Need help with the exact sum of convergent series

1. ## Need help with the exact sum of convergent series

Find the exact sum of the following convergent series:

sum from n=0 to infinity of (2n/(3nn!))

Thanks!

2. ## Re: Need help with the exact sum of convergent series

You should know that \displaystyle \begin{align*} e^x = \sum_{n = 0}^{\infty} \frac{x^n}{n!} \end{align*}.

Notice that \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?

3. ## Re: Need help with the exact sum of convergent series

Is it e^(2/3)?

4. ## Re: Need help with the exact sum of convergent series

Originally Posted by kimsanders82
Is it e^(2/3)?
Yes, well done