Question

\(2^{100}-2^{99}+...+2^2-2\)

Answer 1

ta đặc : \(A=2^{100}-2^{99}+...+2^2-2\)

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

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

\(\Leftrightarrow3A=2^{101}-2\Rightarrow A=\dfrac{2^{101}-2}{3}\)

vậy ..................................................................................................................