Question

$\frac{1}{2}+\frac{2^1}{2^2}+\frac{2^2}{2^3}+.....+\frac{2^{2006}}{2^{2007}}+\frac{2^{2007}}{2^{2008}}$ is equal to

• A. 1004
• B. $\frac{1}{2^{2008}}$
• C. 2008
• D. 502

Answer 1

The correct option is A 1004

$\frac{1}{2}+\frac{2^1}{2^2}+\frac{2^2}{2^3}+.....+\frac{2^{2006}}{2^{2007}}+\frac{2^{2007}}{2^{2008}}$
= $\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+....2008times$
= $\frac{2008}{2}$
= $1004$