Question

Find the sum (pre calc)

Answer 1

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

`\text{The answer is}~ \frac 65`