Question

$\underset{n\to \infty }{lim}\frac{{2.3}^n-{3.5}^n}{{3.3}^n+{4.5}^n}=$

• A. $\frac{2}{3}$
• B. $-\frac{3}{4}$
• C. $1$
• D. $0$

Answer 1

The correct option is B $-\frac{3}{4}$

$\underset{n\to \infty }{lim}\frac{{2.3}^n-{3.5}^n}{{3.3}^n+{4.5}^n}$
$=\underset{n\to \infty }{lim}\frac{5^n(2{\left(\frac{3}{5}\right)}^n-3)}{5^n(3{\left(\frac{3}{5}\right)}^n+4)}$
$Asn\to \infty ,{\left(\frac{3}{5}\right)}^n\to 0$
$=-\frac{3}{4}$