Question

Answer 1

a: \(\dfrac{M}{100}=\dfrac{100^{100}+1}{100^{100}+100}=\dfrac{100^{100}+100-99}{100^{100}+100}=1-\dfrac{99}{100^{100}+100}\)

\(\dfrac{N}{100}=\dfrac{100^{101}+1}{100^{101}+100}=1-\dfrac{99}{100^{101}+100}\)

\(100^{100}+100< 100^{101}+100\)

=>\(\dfrac{99}{100^{100}+100}>\dfrac{99}{100^{101}+100}\)

=>\(-\dfrac{99}{100^{100}+100}< -\dfrac{99}{100^{101}+100}\)

=>\(-\dfrac{99}{100^{100}+100}+1< -\dfrac{99}{100^{101}+100}+1\)

=>\(\dfrac{M}{100}< \dfrac{N}{100}\)

=>M<N

b: \(2008A=\dfrac{2008^{2009}+2008}{2008^{2009}+1}=1+\dfrac{2007}{2008^{2009}+1}\)

\(2008B=\dfrac{2008^{2008}+2008}{2008^{2008}+1}=1+\dfrac{2007}{2008^{2008}+1}\)

Ta có: \(2008^{2009}+1>2008^{2008}+1\)

=>\(\dfrac{2007}{2008^{2009}+1}< \dfrac{2007}{2008^{2008}+1}\)

=>\(\dfrac{2007}{2008^{2009}+1}+1< \dfrac{2007}{2008^{2008}+1}+1\)

=>2008A<2008B

=>A<B