Question

Cho M=2^2025-2^2024-2^2023- ... 2^2-2. 

Giá trị của M bằng

Answer 1

Đặt \(A=2^{2024}+2^{2023}+...+2^2+2\)

=>\(2A=2^{2025}+2^{2024}+...+2^3+2^2\)

=>\(2A-A=2^{2025}+2^{2024}+...+2^2-2^{2024}-2^{2023}-...-2^2-2\)

=>\(A=2^{2025}-2\)

\(M=2^{2025}-2^{2024}-2^{2023}-...-2^2-2\)

\(=2^{2025}-\left(2^{2025}-2\right)\)

=2

Answer 2

Đặt A=22024+22023+...+22+2A=22024+22023+...+22+2

=>2A=22025+22024+...+23+222A=22025+22024+...+23+22

=>2A−A=22025+22024+...+22−22024−22023−...−22−22A−A=22025+22024+...+22−22024−22023−...−22−2

=>A=22025−2A=22025−2

M=22025−22024−22023−...−22−2M=22025−22024−22023−...−22−2

=22025−(22025−2)=22025−(22025−2)

=2