Câu hỏi của Leona

Question

tính M =22010-(22009+22008+...+21+20)

Mashiro Shiina · Accepted Answer

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

Đặt:

$S=2^{2009}+2^{2008}+....+2^1+2^0$

$S=2^0+2^1+.....+2^{2008}+2^{2009}$

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

$2S=2^1+2^2+.....+2^{2009}+2^{2010}$

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

$S=2^{2010}-2^0=2^{2010}-1$

Thay S vào M ta có:

$M=2^{2010}-\left(2^{2010}-1\right)$

$M=2^{2010}-2^{2010}+1=1$Câu trả lời: $M=2^{2010}-\left(2^{2009}+2^{2008}+....+2^1+2^0\right)$

Đặt:

$S=2^{2009}+2^{2008}+....+2^1+2^0$

$S=2^0+2^1+.....+2^{2008}+2^{2009}$

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

$2S=2^1+2^2+.....+2^{2009}+2^{2010}$

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

$S=2^{2010}-2^0=2^{2010}-1$

Thay S vào M ta có:

$M=2^{2010}-\left(2^{2010}-1\right)$

$M=2^{2010}-2^{2010}+1=1$

Trần Đăng Nhất · Answer

M=22010-(22009+22008+22007+...+21+20)

M=22010-22009-22008-22007-...-21-20

=>2M=22011-22010-22009-22008-...-22-21

=>2M-M=22011-22010-22009-22008-...-22-21-(22010-22009-22008-22007-...-21-20)

=>M=22011-22010-22009-22008-...-22-21-22010+22009+22008+22007+...+21+20

=22011-22010-22010+20

=22011-2.22010+1

=22011-22011+1

=1

Vậy M=1Câu trả lời: M=22010-(22009+22008+22007+...+21+20)