\(A=\frac{2003\cdot2004-1}{2003\cdot2004}=1-\frac{1}{2003\cdot2004}\)

\(B=\frac{2004\cdot2005-1}{2004\cdot2005}=1-\frac{1}{2004\cdot2005}\)

Vì 1 = 1 và \(\frac{1}{2003\cdot2004}>\frac{1}{2004\cdot2005}\) nên A > B

Vậy A > B

Chắc sai =))

\(A=\frac{2003\cdot2004-1}{2003\cdot2004}=\frac{2003\cdot2004}{2003\cdot2004}-\frac{1}{2003\cdot2004}=1-\frac{1}{2003\cdot2004}\)

\(B=\frac{2004\cdot2005-1}{2004\cdot2005}=\frac{2004\cdot2005}{2004\cdot2005}-\frac{1}{2004\cdot2005}=1-\frac{1}{2004\cdot2005}\)

có : \(\frac{1}{2003\cdot2004}>\frac{1}{2004\cdot2005}\)

\(\Rightarrow1-\frac{1}{2003\cdot2004}< 1-\frac{1}{2004\cdot2005}\)

\(\Rightarrow A< B\)

\(2004A=\frac{2004^{2004}+2004}{2004^{2004}+1}=1+\frac{2003}{2004^{2004}+1}\)

\(2004B=\frac{2004^{2005}+2004}{2004^{2005}+1}=1+\frac{2003}{2004^{2005}+1}\)

\(\frac{2003}{2004^{2004}+1}>\frac{2003}{2004^{2005}+1}\)

\(\Rightarrow2004A>2004B\)

\(\Rightarrow A>B\)

2004A=\(\frac{2004^{2004}+2004}{2004^{2004}+1}\)

\(\frac{2004^{2004}+2004}{2004^{2004}+1}-1=\frac{2003}{2004^{2004}+1}\)

2004B=\(\frac{2004^{2005}+2004}{2004^{2005}+1}\)

\(\frac{2004^{2005}+2004}{2004^{2005}+1}-1=\frac{2003}{2004^{2005}+1}\)

Ta thấy :\(\frac{2003}{2004^{2004}+1}>\frac{2003}{2004^{2005}+1}\)

=> \(2004A>2004B\)

Vậy \(A>B\)

Có : 2004A = 2004^2004+2004/2004^2004+1 = 1 + 2003/2004^2004+1

2004B = 2004^2005+2004/2004^2005+1 = 1 + 2003/2004^2005+1 < 1 + 2003/2004^2004+1 = 2014A

=> A > B

Tk mk nha

\(B=\frac{2004^{2004}+1}{2004^{2005}+1}< \frac{2004^{2004}+1+2003}{2004^{2005}+1+2003}=\frac{2004^{2004}+2004}{2004^{2005}+2004}=\frac{2004\left(2004^{2003}+1\right)}{2004\left(2004^{2004}+1\right)}=\frac{2004^{2003}+1}{2004^{2004}+1}=A\)

Vậy A > B

tớ có cách khác cũng ra kết quả giống bạn

\(B=\frac{2003+2004}{2004+2005}=\frac{2003}{2004+2005}+\frac{2004}{2004+2005}\)

Ta có: \(\frac{2003}{2004}>\frac{2003}{2004+2005}\)

          \(\frac{2004}{2005}>\frac{2004}{2004+2005}\)

\(\frac{2003}{2004}+\frac{2004}{2005}>\frac{2003+2004}{2004+2005}\)

\(A>B\)

Vậy A>B

đáp án là A>B

chúc bn hok tốt!

                                 \(\text{ Bài giải}\)

\(A=\frac{2003}{2004}+\frac{2004}{2005}=0,999500998 + 0,999501247=1.99900225\)

\(B=\frac{2003+2004}{2004+2005}=\frac{4007}{4009}=0,999501122\)

\(\text{Vì : }1,99900224>0,999501122\text{ nên }A>B\)

        \(\text{Vậy : }A>B\)

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