Question

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

Answer:

2^n + 2^(n-1) = 2^(n-1) [ 2 + 1) = 3 × 2^(n-1)

2^(n+1) - 2^n = 2^n( 2 -1) = 2^n

So, above expression becomes

3× 2^(n-1)/2^n

= 3/2

#answerwithquality #BAL

Answer 2

Answer:

2^n + 2^(n-1) = 2^(n-1) [ 2 + 1) = 3 × 2^(n-1)

2^(n+1) - 2^n = 2^n( 2 -1) = 2^n

So, above expression becomes

3× 2^(n-1)/2^n

= 3/2