Question

[Sieukid Duy]

so sanh a va b biet 

a=[(2009²⁰⁰⁹+1)]:[(2009²⁰¹⁰+1)]

b=[(2009²⁰⁰⁸+1)]:[(2009²⁰⁰⁹+1)]

Answer 1

[Thanh Hằng Nguyễn]

\(2009A=\frac{2009^{2010}+2009}{2009^{2010}+1}=\)\(\frac{2009^{2010}+1+2008}{2009^{2010}+1}=1+\frac{2008}{2009^{2010}+1}\)

\(2009B=\frac{2009^{2009}+2009}{2009^{2009}+1}=\frac{2009^{2009}+1+2008}{2009^{2009}+1}\)\(=1+\frac{2008}{2009^{2009}+1}\)

Vì \(1+\frac{2008}{2009^{2010}+1}< 1+\frac{2008}{2009^{2009}+1}\) \(\Leftrightarrow A< B\)

Answer 2

[KAITO KID 2005]

\(A=\frac{2009^{2009}+1}{2009^{2010}+1}\Rightarrow2009A=\frac{2009^{2010}+2009}{2009^{2010}+1}\)

\(2009A=\frac{2009^{2010}+1}{2009^{2010}+1}+\frac{2008}{2009^{2010}+1}\)

\(2009A=1+\frac{2008}{2009^{2010}+1}\)

..... sory bn mk hơi luwoif chút nên bn tự lm tương tự vs phần B và so sánh nhé!^^