7/2+7/6+7/17=7/20=7/30=7/42
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Đặt biểu thức trên là A
\(\Rightarrow A=7x\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}+\frac{1}{110}\right)\)
Đặt biểu thức trong ngoặc là B
\(\Rightarrow B=\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{9x10}+\frac{1}{10x11}\)
Đây là dạng tính tổng các phân số mà mỗi phân số có:
-Tử số là hiệu của hai thừa số ở mẫu
-Mẫu số của phân số liền sau là tích của hai thừa số mà thừa số thứ nhất là thừa số thứ hai ở mẫu của phân số liền trước
\(B=\frac{2-1}{1x2}+\frac{3-2}{2x3}+\frac{4-3}{3x4}+...+\frac{10-9}{9x10}+\frac{11-10}{10x11}\)
\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
\(B=1-\frac{1}{11}=\frac{10}{11}\Rightarrow A=\frac{70}{11}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{7}{2}+\frac{7}{6}+\frac{7}{12}+\frac{7}{20}+\frac{7}{30}+\frac{7}{42}+\frac{7}{56}+\frac{7}{72}+\frac{7}{90}\)\(\frac{7}{90}\)
=\(\frac{7}{2+6+12+20+30+42+56+72+90}\)
=\(\frac{63}{10}\)
=6.3
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a) \(\dfrac{3}{8}+\dfrac{7}{12}+\dfrac{10}{16}+\dfrac{10}{24}\)
\(=\dfrac{3}{8}+\dfrac{7}{12}+\dfrac{5}{8}+\dfrac{5}{12}\)
\(=\left(\dfrac{3}{8}+\dfrac{5}{8}\right)+\left(\dfrac{7}{12}+\dfrac{5}{12}\right)\)
\(=1+1\)
\(=2\)
b) \(\dfrac{4}{6}+\dfrac{7}{13}+\dfrac{17}{9}+\dfrac{19}{13}+\dfrac{1}{9}+\dfrac{14}{6}\)
\(=\dfrac{2}{3}+\dfrac{7}{13}+\dfrac{17}{9}+\dfrac{19}{13}+\dfrac{1}{9}+\dfrac{7}{3}\)
\(=\left(\dfrac{2}{3}+\dfrac{7}{3}\right)+\left(\dfrac{7}{13}+\dfrac{19}{13}\right)+\left(\dfrac{17}{9}+\dfrac{1}{9}\right)\)
\(=3+2+2\)
\(=7\)
c) \(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\)
\(=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\)
\(=1-\dfrac{1}{7}\)
\(=\dfrac{6}{7}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(m=\frac{3}{2}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}\)
\(m=\frac{2}{3}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}\)
\(m=\frac{5}{4}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}\)
\(m=\frac{4}{5}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}\)
\(m=\frac{7}{6}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}\)
\(m=\frac{6}{7}+\frac{15}{56}-\frac{17}{72}\)
\(m=\frac{9}{8}-\frac{17}{72}\)
\(m=\frac{8}{9}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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\(\frac{7}{2}+\frac{7}{6}+\frac{7}{12}+\frac{7}{20}+\frac{7}{30}+\frac{7}{42}=7\times\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)
\(=7\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}\right)\)
\(=7\times\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(=7\times\left(\frac{1}{1}-\frac{1}{7}\right)=7\times\left(\frac{7}{7}-\frac{1}{7}\right)=7\times\frac{6}{7}=6\)
7\(\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)
7\(\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)
7\(\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{6}-\frac{1}{7}\right)\)
7\(\left(1-\frac{1}{7}\right)\)
7\(.\frac{6}{7}\)
6
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\(\frac{3}{2}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}+\frac{19}{90}\)
\(=\frac{1+2}{1.2}-\frac{2+3}{2.3}+\frac{3+4}{3.4}-\frac{4+5}{4.5}+\frac{5+6}{5.6}-\frac{6+7}{6.7}+\frac{7+8}{7.8}-\frac{8+9}{8.9}+\frac{9+10}{9.10}\)
\(=1+\frac{1}{2}-\frac{1}{2}+\frac{1}{3}+\frac{1}{4}-...-\frac{1}{8}-\frac{1}{9}+\frac{1}{9}+\frac{1}{10}\)
\(=\frac{11}{10}\)
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