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.

\(\frac{1}{x}\)

Correct answer is A

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

\(S_{n} = \frac{1}{1 - x}\)