Find the sum to infinity of the series \(2+\frac{3}{2}+\frac{9}{8}+\frac{27}{32}+......\)
A
1
B
2
C
8
D
4
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
a = 2
r = \(\frac{3}{4}\)
S = \(\frac{a}{1-r}\)
S = \(\frac{2}{1-\frac{3}{4}}\)
= \(\frac{2}{\frac{1}{4}}\)
S = \(\frac{2}{1}\times \frac{4}{1}\)
= 8.
Source: Myschool Past Questions Archive (Record #9234)