Question

$\underset{n\to \infty }{lim}\frac{{3.2}^{n+1}-{4.5}^{n+1}}{{5.2}^n+{7.5}^n}=$

• A. $-\frac{20}{7}$
• B. $\frac{20}{7}$
• C. $\frac{10}{7}$
• D. $-\frac{10}{7}$

Answer 1

The correct option is A $-\frac{20}{7}$

Let $\text{L}=\underset{n\to \infty }{lim}\frac{{3.2}^{n+1}-{4.5}^{n+1}}{{5.2}^n+{7.5}^n}=\underset{n\to \infty }{lim}\frac{{6.2}^n-{20.5}^n}{{5.2}^n+{7.5}^n}$
Divide numerator and denominator by $5^n$
$\therefore \text{L}=\underset{n\to \infty }{lim}\frac{6.{\left(\frac{2}{5}\right)}^n-20}{5.{\left(\frac{2}{5}\right)}^n+7}=\frac{0-20}{0+7}=-\frac{20}{7}$