Question

so sánh :A=1999²⁰⁰⁰+1/1999¹⁹⁹⁹+1 và B=1999¹⁹⁹⁹+1/1999¹⁹⁹⁸+1

Answer 1

\(A=1999^{2000}+\dfrac{1}{1999^{1999}}+1\)

\(B=1999^{1999}+\dfrac{1}{1999^{1998}}+1\)

\(\Rightarrow A-B=1999^{1999}.\left(1999-1\right)+\dfrac{1}{1999^{1998}}.\left(\dfrac{1}{1998}-1\right)\)

\(\Rightarrow A-B=1998.1999^{1999}-\dfrac{1997}{1998}.\dfrac{1}{1999^{1998}}\)

mà \(0< \dfrac{1997}{1998}.\dfrac{1}{1999^{1998}}< 1;1998.1999^{1999}>0\)

\(\Rightarrow A-B=1998.1999^{1999}-\dfrac{1997}{1998}.\dfrac{1}{1999^{1998}}>0\)

\(\Rightarrow A>B\)