Question

please i want step by step explaination

Answer 1

EXPLANATION.

Value of :

$\sf \implies \dfrac{2^{n} + 2^{n - 1} }{2^{n + 1} - 2^{n} }$

As we know that,

Taking 2ⁿ as common from both numerator and denominator, we get.

$\sf \implies \dfrac{2^{n}\bigg(1 + \dfrac{1}{2} \bigg) }{2^{n} (2 - 1)}$

$\sf \implies \dfrac{\bigg(1 + \dfrac{1}{2} \bigg) }{ (2 - 1)}$

$\sf \implies 1 + \dfrac{1}{2} = \dfrac{3}{2}$

$\sf \implies \dfrac{2^{n} + 2^{n - 1} }{2^{n + 1} - 2^{n} } = \dfrac{3}{2}$

Option [B] is correct answer.