Question

Rút gọn \(A=2^{2010}+2^{2009}+2^{2008}+...+2^3+2^2+2\)

Answer 1

\(A=2^{2010}+2^{2009}+...+2^2+2\)

\(\Rightarrow2A=2^{2011}+2^{2010}+...+2^3+2^2\)

\(\Rightarrow2A-A=\left(2^{2011}+2^{2010}+...+2^3+2^2\right)-\left(2^{2010}+2^{2009}+...+2^2+2\right)\)

\(\Rightarrow A=2^{2011}-2\)

Vậy \(A=2^{2011}-2\)