Question

$\underset{n\to \infty }{\lim }\frac{5^{n+1}+3^n-2^{2n}}{5^n+2^n+3^{2n+3}}$ is equal to

• A. 5
• B. 3
• C. 1
• D. 0

Answer 1

Answer: (D)

$\underset{n\to \infty }{\lim }\frac{5^{n+1}+3^n-2^{2n}}{5^n+2^n+3^{2n+3}}$
$=\underset{n\to \infty }{\lim }\frac{5\cdot 5^n+3^n-4^n}{5^n+2^n+27\cdot 9^n}$
$=\underset{n\to \infty }{\lim }\frac{5\cdot \frac{5^n}{9^n}+\frac{3^n}{9^n}-\frac{4^n}{9^n}}{\frac{5^n}{9^n}+\frac{2^n}{9^n}+27}$
$=\frac{0+0-0}{0+0+27}=0$