Find the sum of `n` terms of series `(x+y) + (x^2+ xy +y^2)+(x^3+x^2y+xy^2+y^3)+..................`

Answer

`1/(x-y)[(x^2(x^2-1))/(x-1)-(y^2(y^n-1))/(y-1)]`

Explanation

`(x+y)+(x^(2)+xy+y^(2))+(x^(3)+x^(2)y+xy^2)+y^(3))+…`n terms
`=1/(x-y)[(x+y)(x-y)+(x^(2)+xy+y^(2))(x-y)+…` n terms]
`=1/(x-y)[(x^(2)+x^(3)+…` n terms)-`(y^(2)+y^(3)+…` n terms)]
`1/(x-y)[(x^(2)(x^(n)-1))/(x-1)-(y^(2)(y^(n)-1))/(y-1)]`