Question

M=2²⁰¹⁰-(2²⁰⁰⁹+2²⁰⁰⁸+...+2¹+2⁰)

Tính

Answer 1

Đặt M = 2^2010 - A

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

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

\(A=2^{2010}-1\)

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

\(\Rightarrow M=1\)

Vậy,.............

Answer 2

\(M=2^{2010}-2^{2009}-2^{2008}-...-2-1\)

\(\Rightarrow2M=2^{2011}-2^{2010}-2^{2009}-...-2^2-2\)

\(\Rightarrow2M-M=2^{2011}-2^{2010}-1=2^{2010-1}\)

Answer 3

Đặt A=1+2+2²+...+2²⁰⁰⁹
2A=2+2²+2⁴+...+2²⁰¹⁰
=> 2A-A=2²⁰¹⁰-1
=>A=2²⁰¹⁰-1
=>M=2010-A=1

Answer 4

\(\text{Đặt }M=2^{2010}-A\)

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

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

\(A=2^{2010}-1\)

\(\Rightarrow\text{ }M=2^{2010}-2^{2010}+1\)

\(\Rightarrow\text{ }M=1\)

\(\text{Vậy : }M=1\)

Answer 5

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

Đặt N = 2^2009 + 2^2008 + ...+ 2^1 + 2^0

=> 2N = 2^2010 + 2^2009 + ...+ 2^2 + 2^1

=> 2N-N = 2^2010 - 2^0

N = 2^2010 - 1

Thay N vào M

có: M = 2^2010 - (2^2010 -1) = 2^2010 - 2^2010 + 1 = 1