Encontrar a soma da série $\displaystyle\sum_{n=0}^\infty \left(\dfrac{2}{5^n} - \dfrac{1}{2^n}\right)$.

$\displaystyle\sum_{n=0}^\infty \left(\dfrac{2}{5^n} - \dfrac{1}{2^n}\right) = \displaystyle\sum_{n=0}^\infty \dfrac{2}{5^n} - \displaystyle\sum_{n=0}^\infty \dfrac{1}{2^n} =$

$= \dfrac{2}{1 - \dfrac{1}{5}} - \dfrac{1}{1 - \dfrac{1}{2}} = \dfrac{5}{2} - 2 = \fbox{$\dfrac{1}{2}$}$