Test Index

Indices

© examsnet.com

Question : 83 of 86

Marks: +1, -0

Simplify

\; \frac{2^{n}+2^{n-1}}{2^{n+1}+2^{n}}=

$2^{n+1}$
$2^{n}$
2
$\; \frac{1}{2}$

Solution:

Concept:

Simplify the expression by factoring out the lowest power of

2

from numerator and denominator.

Explanation:

Numerator:

2^{n} + 2^{n-1} = 2^{n-1}(2 + 1) = 2^{n-1} \cdot 3

.

Denominator:

2^{n+1} + 2^{n} = 2^{n}(2 + 1) = 2^{n} \cdot 3

.

Cancel the common factor

3

:

\frac{2^{n-1} \cdot 3}{2^{n} \cdot 3} = \frac{2^{n-1}}{2^{n}} = \frac{1}{2}

.

Answer:

The simplified value is

\frac{1}{2}

, which matches option D.

© examsnet.com

Go to Question:

Prev Question

Next Question