Write the sum in sigma notation LaTeX: \displaystyle 11-\frac{33}{5}+\frac{99}{25}\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{33}{5}}{11}=- \frac{3}{5} . Using LaTeX: \displaystyle a_{1} and LaTeX: \displaystyle r to write in sigma notation gives LaTeX: \displaystyle \sum_{n=1}^{\infty}11\left( - \frac{3}{5} \right)^{n-1} . Using the formula for the sum of an infinite geometric series gives LaTeX: \displaystyle \frac{11}{1-(- \frac{3}{5})}=\frac{55}{8}