Question

$ \underset{n\to \infty }{\mathop{\lim }}\,\,\,\frac{{{2}^{n+1}}+{{3}^{n+1}}}{{{2}^{n}}+{{3}^{n}}} $ is equal to

• A. $ 0 $
• B. $ 1 $
• C. $ 2 $
• D. $ 3 $

Answer 1

The Correct Option is D

$ \underset{n\to \infty }{\mathop{\lim }}\,\,\,\frac{{{2}^{n+1}}+{{3}^{n+1}}}{{{2}^{n}}+{{3}^{n}}} $
$ \underset{n\to \infty }{\mathop{\lim }}\,\,\,\,\frac{{{2.2}^{n}}+{{3.3}^{n}}}{{{2}^{n}}+{{3}^{n}}} $
$ =\underset{n\to \infty }{\mathop{\lim }}\,\,\,\frac{2.{{\left( \frac{2}{3} \right)}^{n}}+3}{{{\left( \frac{2}{3} \right)}^{n}}+1} $
$ =\frac{0+3}{0+1}=3 $