Question

The value of
$\underset{n\to \infty }{lim}(1-\frac{1}{x}+\frac{1}{x^2}-.......n\text{term})$ for all $x\in (-1,1)$ is

• A. $\frac{x}{x-1}$
• B. $\frac{1}{x+1}$
• C. $\frac{x}{x+1}$
• D. $\frac{1}{x-1}$

Answer 1

The correct option is C $\frac{x}{x+1}$

$\underset{n\to \infty }{lim}(1+(-\frac{1}{x})+(-\frac{1}{x}{)}^2+.......n\text{term})$
For $n\to \infty$
$S_{\infty }=\frac{a}{1-r}{S}_{\infty }=\frac{1}{1-(-\frac{1}{x})}=\frac{x}{x+1}$