$\frac{2^{n + 4} - 2 (2^{n})}{2 (2^{n + 3})}$ when simplifies is:

2^{n + 1} - \frac{1}{8}

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- 2^{n + 1}

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1 - 2^{n}

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\frac{7}{8}

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Solution

The correct option is D $\frac{7}{8}$
$\frac{2^{n + 4} - {2.2}^{n}}{{2.2}^{n + 3}} = \frac{2^{n} {.2}^{4} - 2^{n} .2}{{2.2}^{n} {.2}^{3}}$
$= \frac{(2^{4} - 2) (2^{n})}{2^{4} (2^{n})}$
$= \frac{8 - 1}{8} = \frac{7}{8}$

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