Question

The value of $1-\frac{1}{20}+\frac{1}{{20}^2}-\frac{1}{{20}^3}+.....$ correct to 5 places of decimal is

• A. 1.05
• B. 0.95238
• C. 0.95239
• D. 10.5

Answer 1

The correct option is B 0.95238

$\Rightarrow 1-\frac{1}{20}+\frac{1}{{20}^2}-\frac{1}{{20}^3}+....$
$\Rightarrow 1-\frac{1}{20}+\frac{1}{400}-\frac{1}{8000}+....$
$\Rightarrow 1-0.05+0.0025-0.000125+...........$
$\Rightarrow 1.0025-0.050125\Rightarrow 0.952375\Rightarrow 0.95238$