Question

The value of $\frac{2^{n+4}-2\times 2^n}{2\times 2^{(n+3)}}+2^{-3}$ is equal to ...........

• A. $2^{n+1}$
• B. $\left(\begin{array}{c}\frac{9}{8}-2^n\end{array}\right)$
• C. $\left(\begin{array}{c}-2^{n+1}+\frac{1}{8}\end{array}\right)$
• D. $1$

Answer 1

The correct option is D $1$

$\frac{2^{n+4}-2\times 2^n}{2\times 2^{(n+3)}}+2^{-3}$
$\frac{2^{n+4}-2^{n+1}}{2^{(n+4)}}+2^{-3}$
$\frac{2^n(2^4-2^1)}{2^n\times 2^4}+2^{-3}$
$\frac{(2^4-2^1)}{2^4}+2^{-3}$
$\frac{(16-2)}{16}+\frac{1}{8}$
$\frac{14}{16}+\frac{1}{8}$
$\frac{14+2}{16}=1$
Answer (D) 1