The sum of the series `3-1+1/3-1/9+....` is equal to

Options

A. `(20)/(9)`
B. `(9)/(20)`
C. `(9)/(4)`
D. `(4)/(9)`

Answer

C

Explanation

The series is `(3)/(3^(0))-(3)/(3^(1))+(3)/(3^(2))-(3)/(3^(3))+...oo` ltbr. This is a G.P. with first term a=3
and common ratio `r=-(1)/(3)`
`:."Sum "S=(3)/(1-(-(1)/(3)))=(3xx3)/(3+1)=(9)/(4)`