Question

Find the sum (pre calc)

Answer 1

$\text{It is a geometric series.}\\\\\text{First term,}~ a = 2\\\\\text{Common ratio,}~ r = \dfrac{-\tfrac 43}2 = -\dfrac 46 = -\dfrac 23\\\\\text{Sum of an infinite geometric series,}\\\\S_{\infty} = \dfrac{a}{1-r}\\\\\\~~~~~=\dfrac{2}{1-\left(- \dfrac 23 \right)}\\\\\\~~~~~=\dfrac{2}{1+ \dfrac 23}\\\\\\~~~~~=\dfrac{2}{\tfrac 53}\\\\\\~~~~~=\dfrac{6}{5}$

$\text{The answer is}~ \dfrac 65$