For what value of `n ,\ dot(a^(n+1)+b^(n+1))/(a^n+b^n)` is the arithmetic mean of `a\ a n d\ b ?`

Explanation

`(a^(n+1)b^(n+1))/(a^(n)+b^(n))=sqrt(ab)=a^(1//2)b^(1//2)` by given condition
`rArra^(n+1)+b^(n+1)=a^(n)a^(1//2)b^(1//2)+b^(n)b^(1//2)a^(1//2)`
`=a^(n+1//2)sqrtb+b^(n+1//2)sqrta`
`rArra^(n+1)-a^(n+1/2)sqrtb=b^(n+1/2)-sqrta-b^(n+1)`
`rArra^(n+1//2)(sqrta-sqrtb)=b^(n+1//2)(sqrta-sqrtb)`
`rArra^(n+1//2)=b^(n+1//2)`
The above is possible only when
n+1/2=0
`rArrn=-1.2=0`
`rArrn=-1/2`