Question

If $a, x$ are real numbers and $\left|a\right| <1, \left|x\right|<1, then 1+\left(1+a\right)x+\left(1+a+a^{2}\right)x^{2}+.... \infty$ is equal to

• A. $\frac{1}{\left(1-a\right)\left(1-ax\right)}$
• B. $\frac{1}{\left(1-a\right)\left(1-x\right)}$
• C. $\frac{1}{\left(1-x\right)\left(1-ax\right)}$
• D. $\frac{1}{\left(1+ax\right)\left(1-a\right)}$

Answer 1

Answer: (C)

$\frac{1}{1-x}+\frac{ax}{1-x} +\frac{a^{2}x^{2}}{1-x}+ .... =\frac{1}{1-x}\times \left(1+ax+a^{2}x^{2}+ .....\right)=\frac{1}{1-x}. \frac{1}{1-ax}$