Question

Tính nhanh:

B=\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+....+\(\frac{1}{99.100}\)

Answer 1

\(B=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)

\(B=\frac{1}{1}-\frac{1}{100}\)

\(B=\frac{99}{100}\)

Answer 2

\(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{99.100}\)

     \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}\)

        \(=1-\frac{1}{100}\)

          \(=\frac{99}{100}\)