Ta có: \(A=\frac{2}{60\cdot63}+\frac{2}{63\cdot66}+\cdots+\frac{2}{117\cdot120}+\frac{2}{2003}\)

\(=\frac23\left(\frac{3}{60\cdot63}+\frac{3}{63\cdot66}+\cdots+\frac{3}{117\cdot120}\right)+\frac{2}{2003}\)

\(=\frac23\left(\frac{1}{60}-\frac{1}{63}+\frac{1}{63}-\frac{1}{66}+\cdots+\frac{1}{117}-\frac{1}{120}\right)+\frac{2}{2003}\)

\(=\frac23\left(\frac{1}{60}-\frac{1}{120}\right)+\frac{2}{2003}=\frac23\cdot\frac{1}{120}+\frac{2}{2003}=\frac{1}{60\cdot3}+\frac{2}{2003}=2\left(\frac{1}{360}+\frac{1}{2003}\right)\)

TA có: \(B=\frac{5}{40\cdot44}+\frac{5}{44\cdot48}+\cdots+\frac{5}{76\cdot80}+\frac{5}{2003}\)

\(=\frac54\left(\frac{4}{40\cdot44}+\frac{4}{44\cdot48}+\cdots+\frac{4}{76\cdot80}\right)+\frac{5}{2003}\)

\(=\frac54\left(\frac{1}{40}-\frac{1}{44}+\frac{1}{44}-\frac{1}{48}+\cdots+\frac{1}{76}-\frac{1}{80}\right)+\frac{5}{2003}\)

\(=\frac54\left(\frac{1}{40}-\frac{1}{80}\right)+\frac{5}{2003}=\frac54\cdot\frac{1}{80}+\frac{5}{2003}=5\left(\frac{1}{320}+\frac{1}{2003}\right)\)

\(A-B=\frac{2}{360}+\frac{2}{2003}-\frac{5}{320}-\frac{5}{2003}\)

\(=\frac{2}{360}-\frac{5}{320}-\frac{3}{2003}=\frac{2\cdot8-5\cdot9}{2880}-\frac{3}{2003}=\frac{-29}{2880}-\frac{3}{2003}<0\)

=>A<B

khó nhỉ

Bài này cũng dễ mà! Hãy cố gắng lên bạn sẽ làm được mà.

Con Ly Anh Tho kia biết trả lời thì trả lời đi chứ nói như vậy ai mà biết làm.

easy

\(\frac{2}{60}+\frac{2}{63}+\frac{2}{63}+\frac{2}{66}+....+\frac{2}{117}+\frac{2}{120}+\frac{2}{2003}\)