Question

Tinh gia tri bieu thuc A = \(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{99\times100}\)

Answer 1

A = 1/1 x 2 + 1/2 x 3 + 1/3 x 4 + ... + 1/99x 100

A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + .... + 1/99 - 1/100

A =1 - 1/100

A = 99/100

Answer 2

\(\frac{1}{1\times2}+\frac{1}{2\times3}+...........+\frac{1}{99\times100}\)

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

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

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