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1/7+1/91+1/247+1/475+1/775+1/1147=? (1)
ta có: (1) <=>: 1/(1.7)+1/(7.13)+1/(13.19)+1/(19.25)+1/(25.31)+1/(31.37)
=1/6.(1-1/7+1/7-1/13+1/13-1/19+1/19-1/25+1/25-1/31+1/31-1/37)
=1/6.(1-1/37)=6/37
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ta có:
\(S=\frac{4}{6}\left(\frac{6}{1.7}+\frac{6}{7.13}+...+\frac{6}{43.49}\right)\)\(=\frac{4}{6}\left(\frac{7-1}{1.7}+\frac{13-7}{7.13}+...+\frac{49-43}{43.49}\right)=\frac{4}{6}\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{13}+...+\frac{1}{43}-\frac{1}{49}\right)\)
\(\frac{4}{6}\left(1-\frac{1}{49}\right)=\frac{4.48}{6.49}=\frac{32}{49}\)
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đặt biểu thức trên =A
ta có: A=2/13.19+2/19.25+2/25.31+...+2/613.619
=(2/13-2/19)+(2/19-2/25)+(2/25-2/31)+...+(2/613-2/619)
=2/13-2/19+2/19-2/25+2/25-2/31+...+2/613-2/619
=2/13+(2/19-2/19)+(2/25-2/25)+(2/31-2/31)+...+(2/613-2/613)-2/619
=2/13-2/619=1212/8047
Theo như tôi thấy thì phân số sau khi đổi ra đâu bằng phân số ban đầu đâu bạn? ví dụ như: 2/13.19 = ( 2/13 - 2/19) tôi thấy đâu có bằng nhau đâu nhỉ? nếu quy đồng lại ( 2/13 - 2/19) thì nó phải = 12/ 13.19 chứ? đâu phải là 2/13.19 đâu. Bạn có thể giải thích lại cho mình 1 chút được không? chân thành cám ơn bạn
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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)
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\(=\dfrac{1}{7}+\dfrac{4}{6}\left(\dfrac{6}{7\cdot13}+\dfrac{6}{13\cdot19}+...+\dfrac{6}{43\cdot49}\right)\)
\(=\dfrac{1}{7}+\dfrac{2}{3}\left(\dfrac{1}{7}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{19}+...+\dfrac{1}{43}-\dfrac{1}{49}\right)\)
\(=\dfrac{1}{7}+\dfrac{2}{3}\cdot\dfrac{6}{49}=\dfrac{1}{7}+\dfrac{4}{49}=\dfrac{11}{49}\)
![](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 !!!
Nhanh Ken my sang can gap
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