A) \[-1\]
B) \[1\]
C) \[0\]
D) \[\frac{1}{2}\]
Correct Answer: B
Solution :
\[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{a}^{n}}+{{b}^{n}}}{{{a}^{n}}+{{d}^{n}}}\] \[=\underset{n\to \infty }{\mathop{\lim }}\,\frac{1+{{\left( \frac{b}{a} \right)}^{n}}}{1+{{\left( \frac{d}{a} \right)}^{n}}}\] \[=\frac{1+0}{1+0}\] \[\left[ \because \,\,{{\left( \frac{b}{a} \right)}^{n}}\to 0\,\,and\,\,{{\left( \frac{d}{a} \right)}^{n}}\to \,\,as\,\,n\to \infty \right]\] \[=1\]
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