Let $\displaystyle \displaystyle \sum_{n=0}^{\infty} a_{n} x^{n} $ be a convergent series.

Let $\displaystyle S_{n} $ be the nth partial sum of the above series.

Then $\displaystyle \displaystyle \sum^{\infty}_{n=1} S_{n} x^{n} = \frac{1}{1-x} \sum^{\infty}_{n=0} a_{n} x^{n} $ .

Should this be obvious? I don't get it.