A) equals 0
B) equals - 1
C) equals 1
D) does not exist
Correct Answer: B
Solution :
\[\underset{n\to \infty }{\mathop{\lim }}\,\,\frac{{{a}^{n}}+{{b}^{n}}}{{{a}^{n}}-{{b}^{n}}}=\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{\left( \frac{a}{b} \right)}^{n}}+1}{{{\left( \frac{a}{b} \right)}^{n}}-1}\] \[=-1\] \[\left[ \text{since, 0 }\frac{a}{b}<1\,implies\,{{\left( \frac{a}{b} \right)}^{n}}\to 0\,as\,n\to \infty \right]\]
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