tính : A = 1/2 + 1/6 + 1/12 + 1/20 + ... + 1/9900
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
`A=1/2+1/6+1/12+1/20+1/30+...+1/9900`
`=1/(1xx2)+1/(2xx3)+1/(3xx4)+1/(4xx5)+1/(5xx6)+...+1/(99xx100)`
`=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/99-1/100`
`=1/1-1/100`
`=100/100-1/100`
`=99/100`
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(1-\frac{2}{6}\right)\left(1-\frac{2}{12}\right)...\left(1-\frac{2}{9900}\right)\)
\(=\frac{4}{6}.\frac{10}{12}...\frac{9898}{9900}\)
\(=\frac{1.4}{2.3}.\frac{2.5}{3.4}...\frac{98.101}{99.100}\)
\(=\frac{1.2...98}{3.4...100}.\frac{4.5...101}{2.3...99}\)
\(=\frac{2}{99.100}.\frac{100.101}{2.3}\)
\(=\frac{101}{99.3}\)
\(=\frac{101}{297}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có:
1/2+1/6+...+1/9900
=1/1.2+1/2.3...+1/99.100
=1-1/2+1/2-1/3+1/3-...+1/99-1/100
=1-1/100
=99/100
\(A=\frac{1}{2}+\frac{1}{6}+\cdot\cdot\cdot+\frac{1}{9900}\)
\(A=\frac{1}{1\times2}+\frac{1}{2\times3}+\cdot\cdot\cdot+\frac{1}{99\times100}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\cdot\cdot\cdot+\frac{1}{99}-\frac{1}{100}\)
\(A=1-\frac{1}{100}\)
\(A=\frac{99}{100}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
T= 1 - 1/2 + 1/2 - 1/3 + ......+ 1/99 - 1/100
= 1 - 1/100
= 99/100
![](https://rs.olm.vn/images/avt/0.png?1311)
\(t=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(t=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(t=1-\frac{1}{100}=\frac{99}{100}\)
Vậy \(t=\frac{99}{100}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9900}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}=\frac{99}{100}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A= 1-1/2+1/2+1/3 +......+1/99-1/100
=1-1/100
=99/100