Question

${lim}_{n\to \infty }\left(\frac{2^{n+1}+3^{n+1}}{2^n+3^n}\right)$

is equal to

• A. $2$
• B. $3$
• C. $5$
• D. None of these

Answer 1

The correct option is B $3$

Given,

${lim}_{n\to \infty }\left(\frac{2^{n+1}+3^{n+1}}{2^n+3^n}\right)$

$={lim}_{n\to \infty }\left(\frac{\frac{2^{n+1}}{3^n}+3}{{\left(\frac{2}{3}\right)}^n+1}\right)$

$=\frac{{lim}_{n\to \infty }(\frac{2^{n+1}}{3^n}+3)}{{lim}_{n\to \infty }({\left(\frac{2}{3}\right)}^n+1)}$

$=\frac{3}{1}$

$=3$

Hence, this is the answer.