​ Given that x > 0, the sum ∑∞n=1(x/x+1)n-1 equals A. x B. x + 1 C. x/2x+1 D. x+1/2x+1 ​

Question

Given that x > 0, the sum \(\displaystyle\sum_{n=1}^{\infty}(\frac{x}{x+1})^{n-1}\) equals

∑^∞_n=1(x/x+1)^n-1

A. x

B. x + 1

C. x/2x+1

D. x+1/2x+1

Answer 1

The Given sequence becomes an infinite GP where first term a = 1

And common ratio r = \(\frac{x}{x+1}\)

Sum of infinite terms is given by