Question

Rút gọn : B = \(( -5 ) ^0 + ( -5 ) ^ 1 + (-5)^2+(-5)^3+....+(-5)^{49}+(-5)^{50}\)

Answer 1

\(B=\left(-5\right)^0+\left(-5\right)^1+\left(-5\right)^2+\left(-5\right)^3+...+\left(-5\right)^{49}+\left(-5\right)^{50}\\ -5B=\left(-5\right)^1+\left(-5\right)^2+\left(-5\right)^3+\left(-5\right)^4+...+\left(-5\right)^{50}+\left(-5\right)^{51}\\ B+5B=\left[\left(-5\right)^0+\left(-5\right)^1+\left(-5\right)^2+\left(-5\right)^3+...+\left(-5\right)^{49}+\left(-5\right)^{50}\right]-\left[\left(-5\right)^1+\left(-5\right)^2+\left(-5\right)^3+\left(-5\right)^4+...+\left(-5\right)^{50}+\left(-5\right)^{51}\right]\\ 6B=\left(-5\right)^0-\left(-5\right)^{51}\\ B=\frac{1-\left(-5\right)^{51}}{6}\)