Polynomial sum: $x^n+x^{n-1}y+x^{n-2}y^2+x^{n-3}y^3+\dots+xy^{n-1}+y^n$

Question

Find sum of the expression, $$x^n+x^{n-1}y+x^{n-2}y^2+x^{n-3}y^3+\dots+xy^{n-1}+y^n$$ where $x,y$ are real numbers and $n$ is a natural number.

Answer 1

Hint: It’s a geometric progression with common ratio $\dfrac{y}x$.

Answer 2

It is: $$\frac{x^{n+1}-y^{n+1}}{x-y}.$$