Evaluate the infinite series by identifying it as the value of a derivative of a geometric series.

 $\displaystyle {\sum_{{{n}={2}}}^{{\infty}}}\frac{{{n}{\left({n}-{1}\right)}}}{{5}^{{n}}}=$ Preview Question 6  

$\displaystyle$ Hint:  Write it as $\displaystyle {f}{''}{\left(\frac{{1}}{{5}}\right)}$ where $\displaystyle {f{{\left({x}\right)}}}={\sum_{{{n}={0}}}^{\infty}}\frac{{x}^{{n}}}{{25}}$ .