Write the sum in sigma notation LaTeX: \displaystyle -13-\frac{104}{11}-\frac{832}{121}\ldots and then find the sum.

Taking the ratio of the first two terms gives LaTeX: \displaystyle r = \frac{a_2}{a_1}=\frac{- \frac{104}{11}}{-13}=\frac{8}{11} . Using LaTeX: \displaystyle a_{1} and LaTeX: \displaystyle r to write in sigma notation gives LaTeX: \displaystyle \sum_{n=1}^{\infty}-13\left( \frac{8}{11} \right)^{n-1} . Using the formula for the sum of an infinite geometric series gives LaTeX: \displaystyle \frac{-13}{1-(\frac{8}{11})}=- \frac{143}{3}