Question

Evaluate $\underset{n\to \infty }{lim}\frac{{5.2}^{n+2}-{8.5}^{n+2}}{{3.2}^n+{8.5}^n}$

• A. $-\frac{200}{3}$
• B. $-20$
• C. $-25$
• D. $-5$

Answer 1

The correct option is C $-25$

$\underset{n\to \infty }{lim}\frac{{5.2}^n{.2}^2-{8.5}^n{5}^2}{{3.2}^n+{8.5}^n}(\to \frac{\infty }{\infty }\text{form})$
$\underset{n\to \infty }{lim}\frac{5^n(4(\frac{2}{5}{)}^n-8\times 25)}{5^n(3(\frac{2}{5}{)}^n+8)}$
$=\frac{-200}{8}=-25$