Thu gọn: S = 1 + x + x^2 + x^3 + + x^n
Thu gọn: S = 1 + x + x2 + x3 + …. + xn.
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