Tìm số tự nhiên X, biết: ( 1/1.2.3 + 1/2.3.4 + ....+1/8.9.10) x X = 22/45
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NT
0
AK
9 tháng 4 2018
\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right).x=\frac{22}{45}\)
\(\Rightarrow\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right).x=\frac{22}{45}\)
\(\Rightarrow\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{9.10}\right).x=\frac{22}{45}\)
\(\Rightarrow\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{90}\right).x=\frac{22}{45}\)
\(\Rightarrow\frac{1}{2}.\left(\frac{45}{90}-\frac{1}{90}\right).x=\frac{22}{45}\)
\(\Rightarrow\frac{1}{2}.\frac{44}{90}.x=\frac{22}{45}\)
\(\Rightarrow\frac{11}{45}.x=\frac{22}{45}\)
\(\Rightarrow x=\frac{22}{45}:\frac{11}{45}\)
\(\Rightarrow x=\frac{22}{45}.\frac{45}{11}\)
\(\Rightarrow x=2\)
Vậy \(x=2\)
Chúc học tốt !!!
AK
9 tháng 4 2018
Công thức :
\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{6}\right)=\frac{1}{2}.\frac{2}{6}=\frac{1}{6}=\frac{1}{1.2.3}\)
VD ( dễ hiểu )
LN
1
DD
Đoàn Đức Hà
Giáo viên
25 tháng 1 2021
\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\)
\(A=\frac{1}{2}\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+...+\frac{10-8}{8.9.10}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right)\)
\(A=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{9.10}\right)=\frac{11}{45}\).
Phương trình tương đương với:
\(\frac{11}{45}x=\frac{22}{45}\Leftrightarrow x=2\).
NL
23
NN
11 tháng 7 2015
Đặt A bằng Biểu thức trong ngoặc
\(2A=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{10-8}{8.9.10}\)
\(2A=\frac{1}{2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{8.9}-\frac{1}{9.10}=\frac{1}{2}-\frac{1}{9.10}=\frac{44}{90}\)
\(A=\frac{22}{90}\)
\(x=\frac{23}{45}:A=\frac{23}{45}:\frac{22}{90}=\frac{23}{11}=2\frac{1}{11}\)
11 tháng 7 2015
Áp dụng công thức sau mà dải:
\(\frac{1}{x\left(x+1\right)\left(x+2\right)}=\frac{1}{2}\left(\frac{1}{x\left(x+1\right)}-\frac{1}{\left(x+1\right)\left(x+2\right)}\right)\)
D
22 tháng 5 2017
Ta có:
\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right).x=\frac{23}{45}\)
\(\Rightarrow2.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{8.9.10}\right):2.x=\frac{23}{45}\)
\(\Rightarrow\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{8.9.10}\right):2.x=\frac{23}{45}\)
\(\Rightarrow\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right):2.x=\frac{23}{45}\)
\(\Rightarrow\left(\frac{1}{2}-\frac{1}{90}\right):2.x=\frac{23}{45}\)
\(\Rightarrow\frac{11}{45}x=\frac{23}{45}\)
\(\Rightarrow x=\frac{23}{45}\div\frac{11}{45}=\frac{23}{11}\)
Vậy \(x=\frac{23}{11}\)
DP
23 tháng 5 2017
\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right).x=\frac{23}{45}\)
\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right).\frac{1}{2}.x=\frac{23}{45}\)
\(\left(\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{8.9}+\frac{1}{9.10}\right).\frac{1}{2}.x=\frac{23}{45}\)
\(\left(\frac{1}{2}+\frac{1}{6}+....+\frac{1}{72}+\frac{1}{90}\right).\frac{1}{2}.x=\frac{23}{45}\)
\(\left(\frac{1}{2}-\frac{1}{90}\right).\frac{1}{2}.x=\frac{23}{45}\)
\(\frac{22}{45}.\frac{1}{2}x=\frac{23}{45}\)
\(\frac{11}{45}.x=\frac{23}{45}\)
\(x=\frac{23}{45}\div\frac{11}{45}\)
\(x=\frac{23}{11}\)
=> \(x=\frac{23}{11}\)
13 tháng 2 2016
\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{8.9.10}\right).x=\frac{23}{45}\)
\(\Leftrightarrow\left[\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+....+\frac{1}{8.9}-\frac{1}{9.10}\right)\right]x=\frac{23}{45}\)
\(\Leftrightarrow\left[\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{9.10}\right)\right].x=\frac{23}{45}\)
\(\Leftrightarrow\left(\frac{1}{2}.\frac{44}{90}\right).x=\frac{23}{45}\)
\(\Leftrightarrow\frac{11}{45}.x=\frac{23}{45}\Rightarrow x=\frac{23}{45}:\frac{11}{45}=\frac{23}{11}\)
20 tháng 2 2017
nhung sao banj khong phan h ra ro rang,chang nhe den do khong phan h duoc sao
2 tháng 8 2015
\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right).x=\frac{23}{45}\)
\(\Rightarrow2.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right).x=\frac{46}{45}\)
\(=\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{8.9.10}\right).x\)
\(=\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}+\frac{1}{9.10}\right).x\)
\(=\left(\frac{1}{2}-\frac{1}{90}\right).x=\left(\frac{45}{90}-\frac{1}{90}\right)x=\frac{44}{90}.x=\frac{22x}{45}=\frac{46}{45}\)
=> 22x=46
=> x=\(46:22=\frac{23}{11}\)
TN
16 tháng 3 2016
\(\Leftrightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\cdot x=\frac{22}{45}\)
\(\Rightarrow1-\frac{1}{10}.x=\frac{22}{45}\)
\(\Rightarrow\frac{9}{10}.x=\frac{22}{45}\)
\(\Rightarrow x=\frac{22}{45}:\frac{9}{10}\)
\(\Rightarrow x=\frac{22}{45}.\frac{10}{9}=\frac{22.10}{45.9}=\frac{44}{81}\)
=>x=\(\frac{44}{81}\)
