calculus - Finding formula for nth partial sum

I need to find a formula for the nth partial sum of the series:

$2 + \frac 23 + \frac 29 + \frac {2}{27} + .... + \frac {2}{3^{n-1}} + ...$

then I need to use the formula to find the series' sum if the series converges.

The answer from the back of the book is (the formula):

$$\frac {2(1- (\frac 13) ^ n)}{1 - \frac 13}$$

And the series' sum is 3. Any help would be appreciated. Struggling to figure out how to get the formula.

--Edited because I messed up MathJax, fixed now.

Answer

Your series is a G.P. series with first term $2$ and common ratio $\frac{1}{3}$.
So according to the G.P. sum formula, $S_n=\frac{2\left(1-(\frac{1}{3})^n\right)}{1-\frac{1}{3}}=3\left(1-(\frac{1}{3})^n\right)$. As $n\to\infty$, we can easily check that $S_n\to 3$.

Now do you know the G.P. formula?