Question

The least positive integer n such that $1-\frac{2}{3}-\frac{2}{3^2}-.......-\frac{2}{3^{n-1}}<\frac{1}{100},$ is :

• A. 4
• B. 5
• C. 6
• D. 7

Answer 1

Answer: (C)

$1-2\left(\frac{1}{3^1}+\frac{1}{3^2}\dots \dots .\frac{1}{3^{n-1}}\right)<\frac{1}{100}$
$1-2\left(\frac{1}{3}\right)\frac{\left[1-\frac{1}{3^{n-1}}\right]}{\left(\frac{2}{3}\right)}<\frac{1}{100}$
$\Rightarrow 1-1+\frac{1}{3^{n-1}}<\frac{1}{100}$
$100<3^{n-1}$
$n-1=5$
$n=6$