Question

prove it ..............

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Answer 1

Step-by-step explanation:

$\frac{ {2}^{n} + {2}^{n - 1} }{ {2}^{n + 1} - {2}^{n}} = \frac{3}{2} \\LHS = \frac{ {2}^{n} + {2}^{n - 1} }{ {2}^{n + 1} - {2}^{n}} \\ = \frac{ {2}^{n} + {2}^{n} \times {2}^{ - 1} }{ {2}^{n} \times {2}^{1} - {2}^{n}} \\ = \frac{ {2}^{n} (1 + \frac{1}{2}) }{ {2}^{n} (2 - 1)} \\ = \frac{ \frac{2 + 1}{2} }{1} \\ = \frac{3}{2} \\ = RHS$

Thus proved.