Question

The value of $\underset{n\to \infty }{lim}\frac{3^n+2^n}{3^n-2^n}$ is

• A. $-1$
• B. $1$
• C. $0$
• D. $\infty$

Answer 1

The correct option is B $1$

$\underset{n\to \infty }{lim}\frac{3^n+2^n}{3^n-2^n}=\underset{n\to \infty }{lim}\frac{1+{\left(\frac{2}{3}\right)}^n}{1-{\left(\frac{2}{3}\right)}^n}\left[\text{Dividing by}{3}^n\right]=\frac{1+0}{1-0}[\because \frac{2}{3}<1\therefore {\left(\frac{2}{3}\right)}^n\to 0\text{as}n\to \infty ]=1$