a: \(13C=\dfrac{13^{16}+13}{13^{16}+1}=1+\dfrac{12}{13^{16}+1}\)
\(13D=\dfrac{13^{17}+13}{13^{17}+1}=1+\dfrac{12}{13^{17}+1}\)
Vì \(13^{16}+1< 13^{17}+1\)
nên \(\dfrac{12}{13^{16}+1}>\dfrac{12}{13^{17}+1}\)
=>\(\dfrac{12}{13^{16}+1}+1>\dfrac{12}{13^{17}+1}+1\)
=>13C>13D
=>C>D
b: \(\dfrac{E}{1999}=\dfrac{1999^{1999}+1}{1999^{1999}+1999}=1-\dfrac{1998}{1999^{1999}+1999}\)
\(\dfrac{F}{1999}=\dfrac{1999^{2000}+1}{1999^{2000}+1999}=1-\dfrac{1998}{1999^{2000}+1999}\)
Vì \(1999^{1999}+1999< 1999^{2000}+1999\)
nên \(\dfrac{1998}{1999^{1999}+1999}>\dfrac{1998}{1999^{2000}+1999}\)
=>\(-\dfrac{1998}{1999^{1999}+1999}< -\dfrac{1998}{1999^{2000}+1999}\)
=>\(-\dfrac{1998}{1999^{1999}+1999}+1< -\dfrac{1998}{1999^{2000}+1999}+1\)
=>\(\dfrac{E}{1999}< \dfrac{F}{1999}\)
=>E<F
c:
\(\dfrac{G}{100}=\dfrac{100^{100}+1}{100^{100}+100}=1-\dfrac{99}{100^{100}+100}\)
\(\dfrac{H}{100}=\dfrac{100^{69}+1}{100^{69}+100}=1-\dfrac{99}{100^{69}+100}\)
\(100^{100}+100>100^{69}+100\)
=>\(\dfrac{99}{100^{100}+100}< \dfrac{99}{100^{69}+100}\)
=>\(-\dfrac{99}{100^{100}+100}>-\dfrac{99}{100^{69}+100}\)
=>\(-\dfrac{99}{100^{100}+100}+1>-\dfrac{99}{100^{69}+100}+1\)
=>\(\dfrac{G}{100}>\dfrac{H}{100}\)
=>G>H
