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

The correct option is C $6$

We will solve this by using options
Let's take option A ,
For n=4, $1-\frac{2}{3}-\frac{2}{3^2}-\frac{2}{3^3}=\frac{5}{27}<\frac{1}{100}$
Option B,
For n=5,$1-\frac{2}{3}-\frac{2}{3^2}-\frac{2}{3^3}-\frac{2}{3^4}=\frac{13}{81}<\frac{1}{100}$
Option C,
For n=6,$1-\frac{2}{3}-\frac{2}{3^2}-\frac{2}{3^3}-\frac{2}{3^4}-\frac{2}{3^5}=\frac{1}{243}<\frac{1}{100}$

Hence, the least value of n is 6.