Question

[quachtxuanhong23]

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

giải giúp mình nha

Answer 1

[TFBoys_Châu Anh]

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)

= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

=\(1-\frac{1}{100}=\frac{99}{100}\)

Answer 2

[VẪN LÀ KHIÊM]

1*1/2+1/2*1/3+1/3*1/4+.........+1/99*1/100