Question

Thu gọn hộ mk nhé

M=\(2^{100}-2^{99}+2^{98}-2^{97}+...+2-1\)

Answer 1

\(M=2^{100}-2^{99}+2^{98}-2^{97}+...+2-1\)

\(\Rightarrow2M=2\left(2^{100}-2^{99}+2^{98}-2^{97}+...+2-1\right)\)

\(2M=2^{101}-2^{100}+2^{99}-2^{98}+...+2^2-2\)

\(2M+M=3M=2^{101}-2^{100}+2^{99}-2^{98}+...+2^2-2+2^{100}-2^{99}+2^{98}-2^{97}+...+2-1\)

\(3M=2^{101}-1\Leftrightarrow M=\dfrac{2^{101}-1}{3}\) vậy \(M=\dfrac{2^{101}-1}{3}\)

Answer 2

\(M=2^{100}-2^{99}+2^{98}-2^{97}+...+2-1\)

\(2M=2\left(2^{100}-2^{99}+2^{98}-2^{97}+...+2-1\right)\)

\(2M=2^{101}-2^{100}+2^{99}-2^{98}+...+2^2-2\)

\(2M+M=\left(2^{101}-2^{100}+2^{99}-2^{98}+...+2^2-2\right)+\left(2^{100}-2^{99}+2^{98}-2^{97}+...+2-1\right)\)

\(3M=2^{101}-1\)

\(M=\dfrac{2^{101}-1}{3}\)