Problem 43 (difficulty: 3/10)

Prove that the following identity holds for all positive integer \(\displaystyle n\):

\(\displaystyle \frac{x^n -y^n}{x-y}=x^{n-1}+x^{n-2}\cdot y +\ldots +x\cdot y^{n-2} + y^{n-1} \)

Give me another random problem!