Question

rút gọn

A= 2^100 -2^99 +2^98 - 2^97 +........+2^2 -2

Answer 1

Ta có: \(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)

\(\Rightarrow2A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\)

\(\Rightarrow2A+A=\left(2^{101}-2^{100}+...+2^3-2^2\right)+\left(2^{100}-2^{99}+...+2^2-2\right)\)

\(\Leftrightarrow3A=2^{101}-2\)

\(\Rightarrow A=\frac{2^{101}-2}{3}\)