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S=1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+...+1/(1+2+3+4+...+10)
S=1/(2*3/2)+1/(3*4/2)+1/(4*5/2)+...+1/(10*11/2)
S=2(1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+...+1/(10*11)
S=2(1/2-1/3+1/3-1/4+1/4-1/5+...+1/10-1/11)
S=2(1/2-1/11)
S=2*9/22
S=9/11
nho k cho minh voi nha
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a; 7/2+33/7-75/14=20/7
b: 9/2+1/2:11/2=9/2+1/11=101/22
![](https://rs.olm.vn/images/avt/0.png?1311)
Phân số lớn nhất :\(\frac{9}{10}\)
Phân số bé nhất :\(\frac{1}{2}\)
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Câu b
Ta có :x + 3 /1.3 +3/3.5 + 3/5.7+...+3/13.15=2 1/5
X + 2/3.(1-1/3+1/3-1/5+1/5-1/7+...+1/13-1/15)1=11/5
X+2/3.(1-1/15)=11/5
X+ 2/3.14/15=11/5
X + 28/45=11/5
X = 11/5 -28/45
X=71/45
Câu a gợi ý
1/2-1/3/1/6=0
1/2- 1/3 - 1/6 ) x (1/2 + 2/3 + 3/4 +4/5 + .......+ 2019 /2020 ) =0
3/4:x=9/10
X = 3/4:9/10
X = 5/6
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Bài 2:
\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).......\left(1-\frac{1}{2004}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{2003}{2004}\)
\(=\frac{1}{2004}\)
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\(\dfrac{3}{4}\times\dfrac{8}{5}:1\dfrac{1}{6}\)
=\(\dfrac{6}{5}:\) \(\dfrac{7}{6}\)
=\(\dfrac{6}{5}\times\dfrac{6}{7}=\dfrac{36}{35}\)
2\(\dfrac{1}{3}\) x 1\(\dfrac{1}{4}\) -\(\dfrac{7}{5}\)
\(\dfrac{7}{3}\times\dfrac{5}{4}-\) \(\dfrac{7}{5}\)
\(\dfrac{35}{12}-\dfrac{7}{5}\)
\(\dfrac{175}{60}-\dfrac{84}{60}=\dfrac{91}{60}\)
4\(\dfrac{2}{3}+1\dfrac{1}{4} +2\dfrac{1}{3}+2\dfrac{3}{7}\)
(4 +2) + \(\left(\dfrac{2}{3}+\dfrac{1}{3}\right)\) +1\(\dfrac{1}{4}\) + \(2\dfrac{3}{7}\)
6 + 1 + \(\dfrac{5}{4}\) + \(\dfrac{17}{7}\)
7 + \(\dfrac{103}{28}\)
\(\dfrac{299}{28}\)
\(\frac{1}{2}+\frac{4}{5}:\frac{3}{5}-\frac{1}{5}\)
\(=\frac{1}{2}+\frac{4.5}{5.3}-\frac{1}{5}\)
\(=\frac{1}{2}+\frac{4}{3}-\frac{1}{5}\)
\(=\frac{11}{6}-\frac{1}{5}=\frac{49}{30}\)
= \(\frac{1}{2}\)+ \(\frac{20}{15}\)- \(\frac{1}{5}\)
= \(\frac{55}{30}\)- \(\frac{1}{5}\)
= \(\frac{49}{30}\)