Question

A= \(4+2^2+2^3+.....+2^{2005}\)

Chứng tỏ A là 1 lũy thừa của cơ số 2

Answer 1

\(A=2^2+2^2+2^3+...+2^{2005}\\ 2A=2^3+2^3+2^4+...+2^{2006}\\ 2A-A=\left(2^3+2^3+2^4+...+2^{2006}\right)-\left(2^2+2^2+2^3+...+2^{2005}\right)\\ A=2^{2006}\)

Answer 2

Chi tiết:

\(A=4+2^2+2^3+...+2^{2005}\\ 2A=4\cdot2+2^3+2^4+...+2^{2006}\\ 2A-A=\left(4\cdot2+2^3+2^4+...+2^{2006}\right)-\left(4+2^2+2^3+...+2^{2005}\right)\\ A=4\cdot2+2^{2006}-4-2^2=2^{2006}\left(Đpcm\right)\)