Given that x > 0, the sum Σ_(n-1)^∞x/(x+1)^n-1

Question

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

Σ_(n-1)^∞x/(x+1)^n-1

A. x 

B. x + 1 

C. \(\frac{x}{2x+1}\)

D. \(\frac{x+1}{2x+1}\)

Answer 1

THE ANSWER IS B] X+1

Answer 2

Correct answer is  B. x+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