(x-1)(x+x²+x³+…+x^n)=

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(x-1)(x+x²+x³+…+x^n)=

(x-1)(x+x²+x³+…+x^n)=
(x-1)(x+x²+x³+…+x^n)=

(x-1)(x+x²+x³+…+x^n)=
(x-1)(x+x²+x³+…+x^n)=x²+x³+…+x^n+x^(n+1)-(x+x²+x³+…+x^n)=x^(n+1)-x

X^(n+1)-X