\(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+.....+\frac{1}{18\cdot19}+\frac{1}{19\cdot20}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\)
Sau khi lược bỏ,ta còn lại:
\(A=1-\frac{1}{20}=\frac{19}{20}\)