For the series $\dfrac{1}{x+1} + \dfrac{1}{(x+1)^2} + \dfrac{1}{(x+1)^3} + \ldots$, the sum to infinity exists when —

Question

Accepted Answer

$|x + 1| > 1$

Answer

$-1 < x + 1 < 1$

Answer

$x + 1 = 1$

Answer

$x = 0$

For the series 1x+1+1(x+1)2+1(x+1)3+…\dfrac{1}{x+1} + \dfrac{1}{(x+1)^2} + \dfrac{1}{(x+1)^3} + \ldotsx+11​+(x+1)21​+(x+1)31​+…, the sum to infinity exists when —