Đáp án:
`A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{3.5}+ ... +\frac{1}{99.100}`
`A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}`
`A=\frac{1}{2}+(\frac{-1}{3}+1/3)+...+(\frac{-1}{99}+\frac{1}{99})-\frac{1}{100}`
`A=\frac{1}{2}-\frac{1}{100}`
`A=\frac{50}{100}-\frac{1}{100}`
`A=\frac{49}{100}`