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nCr Definitions and Properties

Prove that: 2...

Question

Prove that: $\frac{2^{n} + 2^{n - 1}}{2^{n + 1} - 2^{n}} = \frac{3}{2}$

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Solution

To Prove : $\frac{2^{n} + 2^{n - 1}}{2^{n + 1} - 2^{n}} = \frac{3}{2}$
$RHS = \frac{2^{n} + 2^{n - 1}}{2^{n + 1} - 2^{n}}$

$= \frac{2 \times 2^{n - 1} + 2^{n - 1}}{2 \times 2^{n} - 2^{n}}$

$= \frac{2^{n - 1} (2 + 1)}{2^{n} (2 - 1)}$

$= \frac{3}{2^{[n - (n - 1)]}}$

$= \frac{3}{2}$

$= RHS$
Hence, proved.

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nCr Definitions and Properties

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