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\(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+...+\frac{5}{2017.2023}\)
\(=5.\frac{1}{6}.\left(\frac{6}{1.7}+\frac{6}{7.13}+\frac{6}{13.19}+...+\frac{6}{2017.2023}\right)\)
\(=\frac{5}{6}.\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{19}+...+\frac{1}{2017}-\frac{1}{2023}\right)\)
\(=\frac{5}{6}.\left(1-\frac{1}{2023}\right)\)
\(=\frac{5}{6}.\frac{2022}{2023}\)
\(=\frac{1685}{2023}\)
\(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+...+\frac{5}{2017.2023}\)
\(=\frac{5.6}{1.7.6}+\frac{5.6}{7.13.6}+\frac{5.6}{13.19.6}+.....+\frac{5.6}{2017.2023.6}\)
\(=\frac{5}{6}.\left(\frac{6}{1.7}+\frac{6}{7.13}+\frac{6}{13.19}+...+\frac{6}{2017.2023}\right)\)
\(=\frac{5}{6}.\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+\frac{1}{13}-\frac{1}{19}+...+\frac{1}{2017}-\frac{1}{2023}\right)\)
\(=\frac{5}{6}.\left(1-\frac{1}{2023}\right)\)
\(=\frac{5}{6}.\frac{2022}{2023}\)
\(=\frac{1685}{2023}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt \(A=\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+....+\frac{5}{x.\left(x+6\right)}\)
\(\Rightarrow A=\frac{5}{6}.\left(\frac{6}{1.7}+\frac{6}{7.13}+...+\frac{6}{x.\left(x+6\right)}\right)\)
\(\Rightarrow A=\frac{5}{6}.\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+....+\frac{1}{x}-\frac{1}{x+6}\right)\)
\(\Rightarrow A=\frac{5}{6}.\left(1-\frac{1}{x+6}\right)\)
\(\Rightarrow\frac{5}{6}.\frac{x+5}{x+6}=\frac{10075}{12096}\)
Làm nốt nha
\(\frac{5}{1.7}+\frac{5}{7.13}+...+\frac{5}{x.\left(x+6\right)}=\frac{10075}{12096}\)
\(\Rightarrow\frac{5}{6}.\left(\frac{6}{1.7}+\frac{6}{7.13}+...+\frac{6}{x.\left(x+6\right)}\right)=\frac{10075}{12096}\)
\(\Rightarrow\frac{5}{6}.\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+...+\frac{1}{x}-\frac{1}{x+6}\right)=\frac{10075}{12096}\)
\(\Rightarrow\frac{5}{6}.\left(1-\frac{1}{x+6}\right)=\frac{10075}{12096}\)
\(\Rightarrow1-\frac{1}{x+6}=\frac{10075}{12096}:\frac{5}{6}\)
\(\Rightarrow1-\frac{1}{x+6}=\frac{10075}{12096}.\frac{6}{5}\)
\(\Rightarrow1-\frac{1}{x+6}=\frac{2015}{2016}\)
\(\Rightarrow\frac{1}{x+6}=1-\frac{2015}{2016}\)
\(\Rightarrow\frac{1}{x+6}=\frac{1}{2016}\)
\(\Rightarrow x+6=2016\)
\(\Rightarrow x=2016-6\)
\(\Rightarrow x=2010\)
Chúc bạn học tốt !!!
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Sửa đề:1/1*3+2/3*7+3/7*13+4/13*21+5/21*31
=1/2(2/1*3+4/3*7+6/7*13+8/13*21+10/21*31)
=1/2(1-1/3+1/3-1/7+...+1/21-1/31)
=1/2*30/31=15/31
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :\(\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+...+\frac{5}{601.607}\right)\)\(\ne0\)
\(\Rightarrow x=0\)
\(X:\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+......+\frac{5}{601.607}\right)=0\)
\(\Rightarrow X:\left(\frac{5}{1}-\frac{5}{7}+\frac{5}{7}-\frac{5}{13}+\frac{5}{13}+......+\frac{5}{601}-\frac{5}{607}\right)=0\)
\(\Leftrightarrow X:\left(5-\frac{5}{607}\right)=0\)
\(\Leftrightarrow X:\frac{3030}{607}=0\)
\(\Leftrightarrow X=0\)
CÁCH 2:\(X:\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+....+\frac{5}{601.607}\right)=0\)
\(\Leftrightarrow X=0.\left(\frac{5}{1.7}+\frac{5}{7.13}+\frac{5}{13.19}+....+\frac{5}{601.607}\right)\)
\(\Leftrightarrow X=0\)
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60 : 5 : [390 : ( 13.12 + 13.15 - 7.13 )]
= 60 : 5 : {390 : [ 13 .( 12 + 15 - 7 )]}
= 60 : 5 : {390 : [ 13.20 ]}
= 60 : 5 : {390 : 260}
= 60 : 5 : 1,5
= 12 : 1,5
= 8
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\(\frac{18+18.7}{18}=\frac{18.\left(7+1\right)}{18}=\frac{1.8}{1}=8\)
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57.18-57.13
=57.(18-13)
=57.5
=58