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Bài 1:
a) Ta có: \(13A=\dfrac{13^{16}+13}{13^{16}+1}=1+\dfrac{12}{13^{16}+1}\)
\(13B=\dfrac{13^{17}+13}{13^{17}+1}=1+\dfrac{12}{13^{17}+1}\)
Vì \(\dfrac{12}{13^{16}+1}>\dfrac{12}{13^{17}+1}\Rightarrow1+\dfrac{12}{13^{16}+1}>1+\dfrac{12}{13^{17}+1}\)
\(\Rightarrow13A>13B\)
\(\Rightarrow A>B\)
Vậy A > B
b) Ta có: \(1999C=\dfrac{1999^{2000}+1999}{1999^{2000}+1}=1+\dfrac{1998}{1999^{2000}+1}\)
\(1999D=\dfrac{1999^{1999}+1999}{1999^{1999}+1}=1+\dfrac{1998}{1999^{1999}+1}\)
\(\dfrac{1998}{1999^{2000}+1}< \dfrac{1998}{1999^{1999}+1}\Rightarrow1+\dfrac{1998}{1999^{2000}+1}< 1+\dfrac{1999}{1999^{1999}+1}\)
\(\Rightarrow1999C< 1999D\)
\(\Rightarrow C< D\)
Vậy C < D
ta thấy 19991999 + 1 / 19992000 + 1 < 1 và 1998 > 0
nên ta có: A < 19991999 + 1 + 1998 / 19992000 + 1 + 1998
< 19991999 + 1999 / 19992000 + 1999
< 1999(19991998 + 1) / 1999(19991999 + 1)
< 19991998 + 1 / 19991999 + 1
< B
Vậy A < B
ta có: \(A=\frac{1999^{1999}+1}{1999^{1998}+1}=\frac{1999.\left(1999^{1998}+1\right)-1998}{1999^{1998}+1}=\frac{1999.\left(1999^{1998}+1\right)}{1999^{1998}+1}-\frac{1998}{1999^{1998}+1}\)
\(=1999-\frac{1998}{1999^{1998}+1}\)
\(B=\frac{1999^{2000}+1}{1999^{1999}+1}=\frac{1999.\left(1999^{1999}+1\right)-1998}{1999^{1999}+1}=\frac{1999.\left(1999^{1999}+1\right)}{1999^{1999}+1}-\frac{1998}{1999^{1999}+1}\)
\(=1999-\frac{1998}{1999^{1999}+1}\)
mà \(\frac{1998}{1999^{1998}+1}>\frac{1998}{1999^{1999}+1}\Rightarrow1999-\frac{1998}{1999^{1998}+1}< 1999-\frac{1998}{1999^{1999}+1}\)
\(\Rightarrow A< B\)
\(\left(1+2+3+...+100\right).\left(1^2+2^2+3^3+...+100^2\right).\left(65.111-13.15.37\right)\)
\(=\left(1+2+3+...+100\right).\left(1^2+2^2+3^3+...+100^2\right).\left(7215-7215\right)\)
\(=\left(1+2+3+...+100\right).\left(1^2+2^2+3^3+...+100^2\right).0\)
\(=0\)
\(1999.1999.1998-1998.1998.1999\)
\(=1999.1998.\left(1999-1998\right)\)
\(=1999.1998.1\)
Tham khảo nhé~
\(C=\frac{1999^{2000}+1}{1999^{1999}+1}< \frac{1999^{1999}+1+1998}{1999^{2000}+1+1998}\)
\(=\frac{1999^{1999}+1999}{1999^{2000}+1999}\)
\(=\frac{1999\cdot(1999^{1998}+1)}{1999\cdot(1999^{1999}+1)}\)
\(=\frac{1999^{1999}+1}{1999^{1998}+1}=D\)
Vậy...