Question

$\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}+\frac{1}{2^6}+\frac{1}{2^7}+\frac{1}{2^8}+\frac{1}{2^9}$=___

• A. $1-\frac{1}{2^6}$
• B. $1-\frac{1}{2^5}$
• C. $1-\frac{1}{2^9}$
• D. $2-\frac{1}{2^9}$

Answer 1

The correct option is C

$1-\frac{1}{2^9}$

In general, the sum of the powers $\frac{1}{2},\frac{1}{2^2},\frac{1}{2^3}$ and so on is equal to the last power subtracted from 1