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\(M:N=\frac{\frac{2008}{1}+\frac{2007}{2}+\frac{2006}{3}+...+\frac{2}{2007}+\frac{1}{2008}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2008}+\frac{1}{2009}}\)
Ta có tử số bằng: 2008+2007/2+2006/3+2005/4+…..+2/2007+1/2008
(Phân tích 2008 thành 2008 con số 1 rồi đưa vào các nhóm)
= (1 + 2007/2) + (1 + 2006/3) + (1 + 2005/4) +... + (1 + 2/2007) + ( 1 + 1/2008) + (1)
= 2009/2 + 2009/3 + 2009//4 + ……. + 2009/2007 + 2009/2008 + 2009/2009
= 2009 x (1/2 + 1/3 + 1/4 + ... + 1/2007 + 1/2008 + 1/2009)
Mẫu số: 1/2 + 1/3 + 1/4 + ... + 1/2007 + 1/2008 + 1/2009
\(\Rightarrow M:N=\frac{2009.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2008}+\frac{1}{2009}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{2008}+\frac{1}{2009}}=2009\)
\(x-\dfrac{11}{15}=3+\dfrac{x}{5}\\ \Leftrightarrow\dfrac{4}{5}x=\dfrac{56}{15}\\ \Leftrightarrow x=\dfrac{14}{3}\)
\(\dfrac{2}{5}\times\dfrac{1}{x}+\dfrac{1}{x}\times2+\dfrac{2}{5}=\dfrac{1}{2}\\ \Leftrightarrow\dfrac{12}{5}\times\dfrac{1}{x}=\dfrac{1}{10}\\ \Leftrightarrow\dfrac{1}{x}=\dfrac{1}{24}\\ \Leftrightarrow x=24\)
\(B=2008+\frac{2007}{2}+\frac{2006}{3}+\frac{2005}{4}+...+\frac{2}{2007}+\frac{1}{2008}\)
\(=1+1+\frac{2007}{2}+1+\frac{2006}{3}+...+1+\frac{1}{2008}\)
\(=\frac{2009}{2009}+\frac{2009}{2}+\frac{2009}{3}+...+\frac{2009}{2008}\)
\(=2009\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2008}+\frac{1}{2009}\right)\)
Suy ra \(A=2009\).
ủa bạn tìm j zo
mk thấy co kết qủa rồi mà
\(M=\frac{1}{2}:\left(\frac{1}{3}:\frac{1}{4}:\frac{1}{5}\times\frac{1}{120}\right)=2008\)
\(M=\frac{1}{2}:\left(\frac{1}{3}\times\frac{4}{1}\times\frac{5}{1}\times\frac{1}{120}\right)=2008\)
\(M=\frac{1}{2}:\left(\frac{4}{3}\times\frac{1}{1}\times\frac{1}{24}\right)=2008\)
\(M=\frac{1}{2}:\left(\frac{4}{3}\times\frac{1}{24}\right)=2008\)
\(M=\frac{1}{2}:\left(\frac{1}{3}\times\frac{1}{6}\right)=2008\)
\(M=\frac{1}{2}:\frac{1}{18}=2008\)
\(M=\frac{1}{2}\times\frac{18}{1}=2008\)
\(M=\frac{18}{2}=2008\)
\(M=9=2008\)