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![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)
\(=\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+...+\frac{2}{19\times21}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)
\(=\frac{1}{3}-\frac{1}{21}\)
\(=\frac{7}{21}-\frac{1}{21}\)
\(=\frac{6}{21}\)
Rút gọn kết quả là \(\frac{2}{7}\), k mk nha mk trả lời đầu tiên đó
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có \(B=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)
\(=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)
\(=2.\left(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{19.21}\right)\)
\(=2.\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(=\frac{2}{2}.\left(\frac{1}{3}-\frac{1}{21}\right)\)
\(=\frac{2}{7}\)
Vậy \(B=\frac{2}{7}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(C=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)
\(=\frac{1}{3}-\frac{1}{21}=\frac{7}{21}-\frac{1}{21}=\frac{6}{21}=\frac{2}{7}\)
các bạn.
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+............+\frac{2}{399}\)
\(=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+.......+\frac{2}{19.21}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+..........+\frac{1}{19}-\frac{1}{21}\)
\(=\frac{1}{3}-\frac{1}{21}=\frac{7}{21}-\frac{1}{21}=\frac{6}{21}=\frac{2}{7}\)
Chúc bạn học tốt
\(\frac{2}{15}+\frac{2}{35}+...+\frac{2}{399}\)
\(=2\left(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{19.21}\right)\)
\(=2\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\right)\)
\(=2\left(\frac{1}{3}-\frac{1}{21}\right)\)
\(=2\times\frac{2}{7}=\frac{4}{7}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Lập mẫu các phân số trên thành tích 2 số lẻ liên tiếp.
15=3.5, 35=5.7, 63=7.9,...,399=19.21
Biến đổi mỗi phân số trên thành hiệu 2 phân số có tử là 1, mẫu là 2 thừa số trong mỗi tích trên( phân số mẫu nhỏ-mẫu lớn)
Phần sau bạn tự làm nhé!
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\)
\(A=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)
\(A=2.\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right)\)
\(A=2.\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\right)\)
\(A=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(A=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(A=2.\frac{3}{16}\)
\(A=\frac{3}{8}\)
\(B=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)
\(B=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)
\(B=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)
\(B=\frac{1}{3}-\frac{1}{21}\)
\(B=\frac{2}{7}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{19.21}\)
\(A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\)
\(A=1-\frac{1}{21}\)
\(A=\frac{20}{21}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\frac{4.4}{3.5}.\frac{5.5}{4.6}......\frac{20.20}{19.21}\)
\(=\left(\frac{4.5...20}{3.4....19}\right).\left(\frac{4.5...20}{5.6....21}\right)\)
\(=\frac{20}{3}.\frac{4}{21}\)
\(=\frac{80}{63}\)