Question

T=2^2010-(2^2009+2^2008+...+2^1+2^0)

Answer 1

\(T=2^{2010}-\left(2^{2009}+2^{2008}+...+2^1+2^0\right)\)

\(T=2^{2010}-\left(2^0+2^1+...+2^{2008}+2^{2009}\right)\)

Đặt: \(A=2^0+2^1+....+2^{2008}+2^{2009}\)

\(2A=2\left(2^0+2^1+...+2^{2008}+2^{2009}\right)\)

\(2A=2^1+2^2+....+2^{2009}+2^{2010}\)

\(2A-A=\left(2^1+2^2+...+2^{2009}+2^{2010}\right)-\left(2^0+2^1+....+2^{2008}+2^{2009}\right)\)\(A=2^{2010}-1\)

Thay \(A\) vào \(T\) ta có:

\(T=2^{2010}-2^{2010}+1=1\)