1 cộng 1 = ?
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
1/2 + 1/6 + 1/12 + ... + 1/132
= 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/11.12
= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/11 - 1/12
= 1 - 1/12
= 11/12
1/90 + 1/110 + 1/132 + ... + 1/10100
= 1/9.10 + 1/10.11 + 1/11.12 + ... + 1/100.101
= ... [như trên]
= 1/9 - 1/100
= 49/450
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)
\(=\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{5.4}+\frac{6-5}{5.6}+\frac{7-6}{7.6}+\frac{8-7}{7.8}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)
\(=\frac{1}{2}-\frac{1}{8}=\frac{4}{8}-\frac{1}{8}=\frac{3}{8}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
= 1/1.3+1/3.5+....+1/11.13
= 1-1/3+1/3-1/5+....+1/11-1/13 = 1-1/13 = 12/13
k mk nha
![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(A=\dfrac{5}{7}-\dfrac{2}{7}+\dfrac{8}{11}+\dfrac{3}{11}+\dfrac{1}{2}=\dfrac{3}{7}+\dfrac{1}{2}+1=\dfrac{6+7+14}{14}=\dfrac{27}{14}\)
b: \(B=\dfrac{11}{17}+\dfrac{6}{17}-\dfrac{8}{19}-\dfrac{30}{19}+\dfrac{-3}{4}=1-2-\dfrac{3}{4}=-1-\dfrac{3}{4}=-\dfrac{7}{4}\)
c: \(C=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}=\dfrac{49}{50}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A=1+1/3+1/6+1/10+ ... + 1/45
1/2.A=1/2+1/6+1/12+1/20+ ... + 1/90
1/2.A= 1/1.2+1/2.3+1/3.4+1/4.5+ ... + 1/9.10
1/2A= 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+ ... +1/9-1/10
1/2.A= 1-1/10
1/2.A=9/10
A=(9/10).2
A=9/5
Sai thì thôi đấy
bài này lớp 4 mà mình không làm được nhỉ . mình học dốt dốt quá .
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right)\div2}=\frac{2009}{2011}\)
Đặt tổng vế trái là A
Ta có : \(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right)\div2}\)
\(\frac{1}{2}A=\frac{1}{2}\left(\frac{1}{3}+\frac{1}{6}+...+\frac{1}{x\left(x+1\right)\div2}\right)\)
\(\frac{1}{2}A=\frac{1}{6}+\frac{1}{12}+...+\frac{1}{x\left(x+1\right)}\)
\(\frac{1}{2}A=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\)
\(\frac{1}{2}A=\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+...+\left(\frac{1}{x}-\frac{1}{x+1}\right)\)
\(\frac{1}{2}A=\frac{1}{2}-\frac{1}{x+1}\)
\(A=\left(\frac{1}{2}+\frac{1}{x+1}\right):\frac{1}{2}\)
\(A=1+\frac{1}{\left(x+1\right)\div2}\)
\(\Rightarrow1+\frac{1}{\left(x+1\right)\div2}=\frac{2009}{2011}\)
\(\Rightarrow\frac{1}{\left(x+1\right)\div2}=\frac{2009}{2011}-1=\frac{2009}{2011}-\frac{2011}{2011}=-\frac{2}{2011}\)
\(\Rightarrow-\frac{2}{-\left(x+1\right)}=-\frac{2}{2011}\)
\(\Rightarrow-\left(x+1\right)=2011\)
\(\Rightarrow x+1=-2011\)
\(\Rightarrow x=-2011-1=-2012\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
a: \(\dfrac{25}{42}-\dfrac{20}{63}=\dfrac{75-40}{126}=\dfrac{35}{126}=\dfrac{5}{18}\)
b: \(\dfrac{9}{20}-\dfrac{13}{75}-\dfrac{1}{6}=\dfrac{135}{300}-\dfrac{52}{300}-\dfrac{50}{300}=\dfrac{33}{300}=\dfrac{11}{100}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1/2+1/6+1/12+1/20+...+1/380
=1/1.2+ 1/2.3+ 1/3.4+ 1/4.5+...+ 1/19.20
= 1/1-1/2+ 1/2-1/3+ 1/3-1/4+ 1/4-1/5+...+1/19-1/20
=1-1/29
=29/29-1/29
= 28/29
2 nha bn :)))))