A) 0
B) 1
C) \[-1\]
D) 2
E) none of these
Correct Answer: A
Solution :
\[\because \] \[\frac{{{x}^{n+1}}+{{y}^{n+1}}}{{{x}^{n}}+{{y}^{n}}}=\frac{x+y}{2}\] \[\Rightarrow \] \[2{{x}^{n+1}}+2{{y}^{n+1}}={{x}^{n+1}}+{{x}^{n}}y\] \[+{{y}^{n+1}}+x{{y}^{n}}\] \[\Rightarrow \] \[{{x}^{n+1}}-{{x}^{n}}y+{{y}^{n+1}}-x{{y}^{n}}=0\] \[\Rightarrow \] \[{{x}^{n}}(x-y)-{{y}^{n}}(x-y)=0\] \[\Rightarrow \] \[(x-y)({{x}^{n}}-{{y}^{n}})=0\] \[\Rightarrow \] \[{{x}^{n}}={{y}^{n}}\] \[(\because x\ne y)\] \[\Rightarrow \] \[n=0\]You need to login to perform this action.
You will be redirected in
3 sec