Question

If $p$ is positive, then the sum to infinity of the series, $\frac{1}{1+p}-\frac{1-p}{{(1+p)}^2}+\frac{{(1-p)}^2}{{(1+p)}^3}-......$ is

• A. $1/2$
• B. $3/4$
• C. $1$
• D. None of these

Answer 1

The correct option is A $1/2$

$a=\frac{1}{1+P}r=-\frac{1-P}{1+P}$

Sum to infinity $=\frac{a}{1-r}=\frac{\frac{1}{1+P}}{1+\frac{1-P}{1+P}}=\frac{\frac{1}{1+P}}{\frac{1+P+1-P}{1+P}}=\frac{1}{2}$