Question

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

Answer 1

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

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

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

\(\Rightarrow3A=2^{101}-2\)

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

   Vậy ......

Answer 2

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

\(\Rightarrow2A+A=2^{101}-2\)

\(\Rightarrow3A=2^{101}-2\)

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