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![](https://rs.olm.vn/images/avt/0.png?1311)
= 3/2*4/3*5/4*6/5*...*999/998*1000/999
rút gọn ta được : 1000/2=500
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1\frac{1}{2}.1\frac{1}{3}.1\frac{1}{4}....1\frac{1}{999}=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{1000}{999}=\frac{3.4.5.6...1000}{2.3.4...999}=\frac{1000}{2}=500\)
\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{1000}{999}\)
\(=\frac{3.4.5...1000}{2.3.4...999}=\frac{1000}{2}=500\)
![](https://rs.olm.vn/images/avt/0.png?1311)
giải
=3/2 . 4/3 . 5/4 .... 1000/999 ( rút gọn ngoài nháp)
=1000/2
= 500
![](https://rs.olm.vn/images/avt/0.png?1311)
=1/1*2+1/2*3+...+1/999*1000
=1/1-1/2+1/2-1/3+...+1/999-1/1000
=1-1/1000
So sánh A và B biết;
A = \(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{999}{1000}\)
B = \(\frac{2}{3}.\frac{3}{4}.\frac{4}{5}...\frac{998}{999}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1\frac{1}{2}.1\frac{1}{3}.1\frac{1}{4}.....1\frac{1}{999}=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}....\frac{1000}{999}=\frac{3.4.5...1000}{2.3.4....999}=\frac{1000}{2}=500\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(D=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{998}{999}.\frac{999}{1000}\)
\(D=\frac{1}{1000}\)( rút gọn những thừa số giống nhau ở tử và mẫu)
Vậy \(D=\frac{1}{1000}\)
D = \(\frac{1}{2}\times\frac{2}{3}\times...\times\frac{999}{1000}\)
D = \(\frac{1}{1000}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
2,
\(\frac{1}{2}.1+\frac{1}{2}.\frac{1}{3}+\frac{1}{3}.\frac{1}{4}+...+\frac{1}{999}.\frac{1}{1000}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}....+\frac{1}{999}-\frac{1}{1000}\)
\(=1-\frac{1}{1000}\)
\(=\frac{999}{1000}\)
\(1\frac{1}{2}.1\frac{1}{3}.1\frac{1}{4}.1\frac{1}{5}.....1\frac{1}{999}\)
\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.\frac{6}{5}....\frac{1000}{999}\)
\(=\frac{1000}{2}\)
\(=500\)