A) \[0\]
B) \[1\]
C) \[2\]
D) \[3\]
Correct Answer: D
Solution :
\[\underset{n\to \infty }{\mathop{\lim }}\,\,\,\frac{{{2}^{n+1}}+{{3}^{n+1}}}{{{2}^{n}}+{{3}^{n}}}\] \[\underset{n\to \infty }{\mathop{\lim }}\,\,\,\,\frac{{{2.2}^{n}}+{{3.3}^{n}}}{{{2}^{n}}+{{3}^{n}}}\] \[=\underset{n\to \infty }{\mathop{\lim }}\,\,\,\frac{2.{{\left( \frac{2}{3} \right)}^{n}}+3}{{{\left( \frac{2}{3} \right)}^{n}}+1}\] \[=\frac{0+3}{0+1}=3\]
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