12.2 #17

Is this geometric series convergent? If so, what is its sum?

\sum\limits_{n=1}^{\infty} \frac{-3^{n-1}}{4^n}=\sum\limits_{n=1}^{\infty} \frac{1}{4}*\frac{-3}{4}^{n-1}

a=\frac{1}{4}, r=\frac{-3}{4}

s=\frac{\frac{1}{4}}{1+\frac{3}{4}} = \frac{1}{4}*\frac{4}{7} = \frac{1}{7}