1+1+1+1+1+1+1 nhân 100 =
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a) (456x35+65x456):19
=456x(65+35):19
=456x100:19
=45600:19
=2400
k mình nhé
Chúc bạn học giỏi
![](https://rs.olm.vn/images/avt/0.png?1311)
`A=1/(1xx2)+1/(2xx3)+1/(3xx4)+...+1/(99xx100)`
`=> A=(2-1)/(1xx2)+(3-2)/(2xx3)+...+(100-99)/(99xx100)`
`=> A=1-1/2+1/2-1/3+...+1/99-1/100`
`=> A=1-1/100`
`=> A=99/100
Sửa đề:
A = 1/(1.2) + 1/(2.3) + 1/(3.4) + ... + 1/(97.98) + 1/(98.99) + 1/(99.100)
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/97 - 1/98 + 1/98 - 1/99 + 1/99 - 1/100
= 1 - 1/100
= 99/100
![](https://rs.olm.vn/images/avt/0.png?1311)
C = 8/9 x 15/16 x 24/25 x ... x 99/100
= 2.4/3.3 x 3.5/4.4 x 4.6/5.5 x ... x 9.11/10.10
= (2.3.4...9) x (4.5.6...11) / (3.4.5...10) x (3.4.5...10)
Gian uoc ta co
= 2.11/10.4
= 11/20
![](https://rs.olm.vn/images/avt/0.png?1311)
Em ơi chỗ 1/100 sửa lại thành 1/110 nha
B=\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}+\frac{1}{110}\)
=\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}\)(Dấu . là nhân nha)
Áp dugj tổng quát \(\frac{1}{x\left(x+1\right)}=\frac{1}{x}-\frac{1}{x+1}\)ta có:
B=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
=\(\frac{1}{2}-\frac{1}{11}\)=\(\frac{9}{22}\)
H=\(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\cdot\cdot\left(1-\frac{1}{2004}\right)\)
=\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\cdot\cdot\frac{2003}{2004}\)
=\(\frac{1}{2004}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : \(\left(1-\frac{1}{99}\right)\text{ x }\left(1-\frac{1}{100}\right)\text{ x }.....\text{ x }\left(1-\frac{1}{2006}\right)\)
\(=\frac{98}{99}\text{ x }\frac{99}{100}\text{ x }\frac{100}{101}\text{ x }......\text{ x }\frac{2005}{2006}\)
\(=\frac{98\text{ x }99\text{ x }100\text{ x }......\text{ x }2005}{99\text{ x }100\text{ x }101\text{ x }......\text{ x }2006}\)
\(=\frac{98}{2006}=\frac{49}{1003}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)....\left(1-\frac{1}{100}\right)=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{99}{100}=\frac{3.8.15...99}{4.9.16...100}\)
\(=\frac{1.3.2.4.3.5...9.11}{2.2.3.3.4.4...10.10}=\frac{\left(1.2.3...9\right)\left(3.4.5...11\right)}{\left(2.3.4...10\right)\left(2.3.4...10\right)}=\frac{1.11}{10.2}=\frac{11}{20}\)
Bài làm:
Ta có: \(\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)...\left(1-\frac{1}{100}\right)\)
\(=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{99}{100}\)
\(=\frac{1.3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}...\frac{9.11}{10^2}\)
\(=\frac{\left(1.2.3...9\right)\left(3.4.5...11\right)}{\left(2.3.4...10\right)\left(2.3.4...10\right)}=\frac{11}{10.2}=\frac{11}{20}\)
Học tốt!!!!
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}=\frac{99}{100}\)
1+1+1+1+1+1+1 =1x7=7
7x100=700
k mnih nhe
= 700 nhaaaaaaaaaaa