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ta có : M = \(\left(1-\frac{1}{8}\right)+\left(1-\frac{2}{9}\right)+\left(1-\frac{3}{10}\right)+...+\left(1-\frac{2009}{2016}\right)\)
M = \(\frac{7}{8}+\frac{7}{9}+\frac{7}{10}+...+\frac{7}{2016}\)
M = \(\frac{21}{24}+\frac{21}{27}+\frac{21}{30}+........+\frac{21}{6048}\)
M = \(21\cdot\left(\frac{1}{24}+\frac{1}{27}+\frac{1}{30}+....+\frac{1}{6048}\right)\)
=> \(\frac{M}{N}=21\)
M=102009+2/102009-1=102009-1+3/102009-1=1+3/102009-1
N=102009/102009-3=102009-3+3/102009-3=1+3/102009-3
vì 102009-1>102009-3
=>m<n
a,Ta co:\(A=\frac{2005^{2005}+1}{2005^{2006}+1}<\frac{2005^{2005}+1+2004}{2005^{2006}+1+2004}=\frac{2005^{2005}+2005}{2005^{2006}+2005}\)
\(=\frac{2005\left(2005^{2004}+1\right)}{2005\left(2005^{2005}+1\right)}=\frac{2005^{2004}+1}{2005^{2005}+1}\) =B Vay A<B
b,lam tuong tu nhu y a
a) A= 1/2010+1+2/2009+1+3/2008+1+...+2009/2+1+1
= 2011/2010+20011/2009+2011/2008+...+2011/2+2011/2011
= 2011(1/2+1/3+1/4+...+1/2011)
Ta có: B= 1/2+1/3+1/4+...+1/2011
suy ra A/B= 2011