The sum of the progression is 1 + x + x2 + x3 + ......
A
\(\frac{1}{1 - x}\)
B
\(\frac{1}{1 + x}\)
C
\(\frac{1}{x - 1}\)
D
\(\frac{1}{x}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Sum of n terms of Geometric progression is \(S_{n} = \frac{a(1 - r^n)}{1 - r}\)
In the given series, a (the first term) = 1 and r (the common ratio) = x.
\(S_{n} = \frac{1(1 - x^{n})}{1 - x}\)
a = 1, and as n tends to infinity
\(S_{n} = \frac{1}{1 - x}\)
Source: Myschool Past Questions Archive (Record #32689)