Thu gọn: S = 1 + x + x^2 + x^3 + + x^n

S = 1 + x + x² + x³ + …. + xⁿ

⇔ S = x⁰ + x¹ + x² + x³ + ...... + xⁿ

⇒ xS = x¹ + x² + x³ + ...... + xⁿ⁺¹

⇒ xS – S = x¹ + x² + x³ + ...... + xⁿ⁺¹ – (x⁰ + x¹ + x² + x³ + ...... + xⁿ)

⇔ S(x – 1) = x¹ + x² + x³ + ...... + xⁿ⁺¹ – x⁰ – x¹ – x² – x³ – …... – xⁿ

⇔ S(x – 1) = xⁿ⁺¹ – x⁰

⇔ S(x–1) = xⁿ⁺¹ – 1