The sum of the series is given by option D.
A sequence of numbers such that the consecutive term is increasing or decreasing by a fixed ratio is called a geometric series.
The series is
7/9+7/27+7/81+1/243 +.................
The common ratio is
(7/27) / (7/9) = 1/3
r < 1
The sum of the geometric series when r < 1 is given by
Sn = a ( 1-rⁿ)
Sn = [tex]\rm \lim_{n \to \infty}[/tex] (7/9) ( 1- (1/3)ⁿ)
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