Câu hỏi của Chu Phương Đông

Question

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

Minh Anh · Accepted Answer

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

Khoá học trên OLM (olm.vn)

Khoá học trên OLM (olm.vn)