The series ${\displaystyle \underset{1}{\overset{}{}}}(-\frac{4}{5}{)}^{k-1}={\displaystyle \underset{1}{\overset{}{}}}(-1{)}^{k-1}{a}_k$converges $by$ the alternating series test. Use theroem $9\mathrm{.}9to$ find how many terms give a partial sum, $S_n$ within $0\mathrm{.}01of$ the sum, $of$ the series