A) 1
B) -1/2
C) 1/2
D) 2
Correct Answer: B
Solution :
As given \[\frac{{{a}^{n+1}}+{{b}^{n+1}}}{{{a}^{n}}+{{b}^{n}}}={{(ab)}^{1/2}}\] \[\Rightarrow \] \[{{a}^{n+1}}-{{a}^{n+1/2}}{{b}^{1/2}}+{{b}^{n+1}}-{{a}^{1/2}}{{b}^{n+1/2}}=0\] \[\Rightarrow \] \[({{a}^{n+1/2}}-{{b}^{n+1/2}})({{a}^{1/2}}-{{b}^{1/2}})=0\] \[\Rightarrow \] \[{{a}^{n+1/2}}-{{b}^{n+1/2}}=0\] \[(\because \ a\ne b\Rightarrow {{a}^{1/2}}\ne {{b}^{1/2}})\] \[\Rightarrow \] \[{{\left( \frac{a}{b} \right)}^{n+1/2}}=1={{\left( \frac{a}{b} \right)}^{0}}\Rightarrow n+\frac{1}{2}=0\Rightarrow n=-\frac{1}{2}\].
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