Ta có:\(B=\frac{2000}{2001+2002}+\frac{2001}{2001-2002}\)
Vì:\(\frac{2000}{2001}>\frac{2000}{2001+2002}\)
\(\frac{2001}{2002}>\frac{2001}{2001+2002}\)
\(\Rightarrow\left(\frac{2000}{2001}+\frac{2001}{2002}\right)>\left(\frac{2000}{2001-2002}-\frac{2001}{2001+2001}\right)\)
\(\Rightarrow A>B\)