2/3 + 2/15 + 2/35 + 2/63
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\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}=2\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)=2\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}\right)\)
\(=2\left[\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\right)\right]\)
\(=2.\left[\frac{1}{2}.\left(1-\frac{1}{9}\right)\right]=2.\left(\frac{1}{2}.\frac{8}{9}\right)=2.\frac{4}{9}=\frac{8}{9}\)
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2/3 + 2/15 + 2/35 + 2/63 + 2/99
= 2/1×3 + 2/3×5 + 2/5×7 + 2/7×9 + 2/9×11
= 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11
= 1 - 1/11
= 10/11
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\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{143}\)
\(=\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+...+\frac{2}{11\times13}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{11}-\frac{1}{13}\)
\(=1-\frac{1}{13}=\frac{12}{13}\)
Đặt \(A=\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+...+\frac{2}{143}\)
\(\Rightarrow A=\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{11.13}\)
\(\Rightarrow A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\)
\(\Rightarrow A=1-\frac{1}{13}=\frac{13}{13}-\frac{1}{13}=\frac{2}{13}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}\)
\(=2.\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right)\)
\(=2.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{9}-\frac{1}{11}\right)\)
\(=2.\left(\frac{1}{1}-\frac{1}{11}\right)\)
\(=\frac{20}{11}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}\)
= \(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}\)
= \(\frac{3-1}{1\times3}+\frac{5-3}{3\times5}+\frac{7-5}{5\times7}+\frac{9-7}{7\times9}+\frac{11-9}{9\times11}\)
= \(\frac{3}{1\times3}-\frac{1}{1\times3}+\frac{5}{3\times5}-\frac{3}{3\times5}+...+\frac{11}{9\times11}-\frac{9}{9\times11}\)
= \(1-\frac{1}{11}\)=\(\frac{10}{11}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}\)
\(=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)
\(=\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+\frac{9-7}{7.9}+\frac{11-9}{9.11}\)
\(=\frac{3}{1.3}-\frac{1}{1.3}+\frac{5}{3.5}-\frac{3}{3.5}+\frac{7}{5.7}-\frac{5}{5.7}+\frac{9}{7.9}-\frac{7}{7.9}+\frac{11}{9.11}-\frac{9}{9.11}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)
\(=1-\frac{1}{11}=\frac{10}{11}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
mi tích tau tau tích mi xong tau trả lời nka việt nam nói là làm
![](https://rs.olm.vn/images/avt/0.png?1311)
2/3 + 2/15 + 2/35 + 2/63
= 2/1×3 + 2/3×5 + 2/5×7 + 2/7×9
= 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9
= 1 - 1/9
= 8/9
Ngược ngược nỗi j, cái này là TÍNH NHANH
Ủng hộ mk nha ♡_♡
a) 2/3+2/15+2/35+2/63
=2/1x3+2/3x5+2/5x7+2/7x9
=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9
=1-1/9
= 8/9.
mả cha mày
2/3 + 2/15 + 2/35 + 2/63
= 2/1×3 + 2/3×5 + 2/5×7 + 2/7×9
= 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9
= 1 - 1/9
= 8/9