\(\frac{M+5}{M+7}=\frac{M+7-2}{M+7}=1-\frac{2}{M+7}\)

\(\frac{M+2005}{M+2007}=\frac{M+2007-2}{M+2007}=1-\frac{2}{M+2007}\)

vì \(\frac{2}{M+7}>\frac{2}{M+2007}\Rightarrow\frac{M+5}{M+7}< \frac{M+2005}{M+2007}\)

Phân số \(\frac{m+6}{m+8}\)lớn hơn .Đúng không ?

m+6/m+8 lon hon

\(\frac{1941}{1931}=1+\frac{1}{1931}\)

\(\frac{2011}{2010}=1+\frac{1}{2010}\)

\(vi\frac{1}{1931}>\frac{1}{2010}->\frac{1941}{1931}>\frac{1}{2010}->\frac{-1941}{1931}< \frac{-2011}{2010}\)

Chọn phân số trung gian: -1

Vì \(\frac{-1941}{1931}>\frac{-1931}{1931}\)   và     \(\frac{-2011}{2010}< \frac{-2010}{2010}\)

\(=>\frac{-1941}{1931}>-1>\frac{-2011}{2010}\)

\(=>\frac{-1941}{1931}>\frac{-2011}{2010}\)

Hay \(M>N\)

Ta có:

1 = \(\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+............+\frac{1}{10}\)(10 phân số \(\frac{1}{10}\))

Mà \(\frac{1}{2}>\frac{1}{10};\frac{2}{3}>\frac{1}{10};............;\frac{9}{10}>10\)

\(\Rightarrow M>1\)

Vậy M > 1

Ta có:

1/2=0,5

2/3>0,6

<=>1/2+2/3>1,1>1

<=>1/2+2/3+3/4+...+9/10>1

Vì 1 = \(\frac{1}{10}+\frac{1}{10}+...+\frac{1}{10}\)

\(\Rightarrow\)M > 1 vì \(\frac{1}{2}>\frac{1}{10};\frac{2}{3}>\frac{1}{10};...;\frac{9}{10}>\frac{1}{10}\)

\(\Rightarrow M>1\)