3 / 2 * 6 + 3/6*10 + 3/ 10 *14+....+ 3/ 26*30
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nhóm cứ hai số liên tiếp lại vs nhâu sẽ đk quy luật tổng của toàn số -2
A=2-4+6-8+10-12+14-16+18-20+22-24+26-28+30-32
A= (-2)+(-2)+(-2)+(-2)+(-2)+(-2)+(-2)+(-2)
A= -16
a) Ta có: \(\dfrac{-5}{7}\left(\dfrac{14}{5}-\dfrac{7}{10}\right):\left|-\dfrac{2}{3}\right|-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)+\dfrac{10}{3}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)\)
\(=\dfrac{-5}{7}\cdot\dfrac{3}{2}\cdot\dfrac{21}{10}-\dfrac{3}{4}\cdot\dfrac{56}{3}+\dfrac{10}{3}\cdot\dfrac{8}{15}\)
\(=\dfrac{-9}{4}-14+\dfrac{16}{9}\)
\(=\dfrac{-1621}{126}\)
b) Ta có: \(\dfrac{17}{-26}\cdot\left(\dfrac{1}{6}-\dfrac{5}{3}\right):\dfrac{17}{13}-\dfrac{20}{3}\left(\dfrac{2}{5}-\dfrac{1}{4}\right)+\dfrac{2}{3}\left(\dfrac{6}{5}-\dfrac{9}{2}\right)\)
\(=\dfrac{-17}{26}\cdot\dfrac{13}{17}\cdot\dfrac{-3}{2}-\dfrac{20}{3}\cdot\dfrac{3}{20}+\dfrac{2}{3}\cdot\dfrac{-33}{10}\)
\(=\dfrac{3}{4}-1-\dfrac{11}{5}\)
\(=-\dfrac{49}{20}\)
1+2+3+4+5+6+7+8+9+10=55
11+12+13+14+15+16+17+18+19+20=155
1+2+3+4+5+6+7+8+9+10+11+12+13+14 +15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30-50-53=362
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30 =465
\(3\div\frac{1}{2}=3\times\frac{2}{1}=6\)
\(\frac{1}{2}\div3=\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}\)
2.Tính theo mẫu :
b) \(\frac{6}{25}\div\frac{21}{20}=\frac{6}{25}\times\frac{20}{21}=\frac{6\times20}{25\times21}=\frac{2\times3\times4\times5}{5\times5\times3\times7}=\frac{8}{35}\)
\(\frac{40}{7}\times\frac{14}{5}=\frac{40\times14}{7\times5}=\frac{5\times8\times7\times2}{7\times5}=16\)
\(\frac{17}{13}\div\frac{51}{26}=\frac{17}{13}\times\frac{26}{51}=\frac{17\times13\times2}{13\times17\times3}=\frac{2}{3}\)
Chúc bạn hok tốt !
\(\frac{3}{2.6}+\frac{3}{6.10}+\frac{3}{10.14}+...+\frac{3}{26.30}=\frac{3}{4}\left(\frac{4}{2.6}+\frac{4}{6.10}+\frac{4}{10.14}+...+\frac{4}{26.30}\right)\)
\(=\frac{3}{4}\left(\frac{1}{2}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+\frac{1}{10}-\frac{1}{14}+...+\frac{1}{26}-\frac{1}{30}\right)=\frac{3}{4}\left(\frac{1}{2}-\frac{1}{30}\right)\)
\(=\frac{3}{4}.\frac{7}{15}=\frac{7}{20}\)
Trả lời:
\(\frac{3}{2\cdot6}+\frac{3}{6\cdot10}+\frac{3}{10\cdot14}+...+\frac{3}{26\cdot30}\)
\(=\frac{3\cdot4}{2\cdot6\cdot4}+\frac{3\cdot4}{6\cdot10\cdot4}+\frac{3\cdot4}{10\cdot14\cdot4}+...+\frac{3\cdot4}{26\cdot30\cdot4}\)
\(=\frac{3}{4}\left(\frac{4}{2\cdot6}+\frac{4}{6\cdot10}+\frac{4}{10\cdot14}+...+\frac{4}{26\cdot30}\right)\)
\(=\frac{3}{4}\cdot\left(\frac{1}{2}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+\frac{1}{10}-\frac{1}{14}+...+\frac{1}{26}-\frac{1}{30}\right)\)
\(=\frac{3}{4}\cdot\left(\frac{1}{2}-\frac{1}{30}\right)\)
\(=\frac{3}{4}\cdot\left(\frac{15}{30}-\frac{1}{30}\right)\)
\(=\frac{3}{4}\cdot\frac{7}{15}\)
\(=\frac{7}{20}\)