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Ta có:
\(\dfrac{1}{3}\times\dfrac{12}{12}=\dfrac{12}{36};\)
\(\dfrac{1}{6}\times\dfrac{6}{6}=\dfrac{6}{36};\)
\(\dfrac{1}{10}\times\dfrac{3}{3}=\dfrac{3}{30};\)
\(\dfrac{1}{15}\times\dfrac{2}{2}=\dfrac{2}{30};\)
\(\dfrac{1}{21}\times\dfrac{4}{4}=\dfrac{4}{84};\)
\(\dfrac{1}{28}\times\dfrac{3}{3}=\dfrac{3}{84};\)
\(A=\dfrac{12}{36}+\dfrac{6}{36}+\dfrac{3}{30}+\dfrac{2}{30}+\dfrac{4}{84}+\dfrac{3}{84}+\dfrac{1}{36}\)
\(=\left(\dfrac{12}{36}+\dfrac{6}{36}+\dfrac{1}{36}\right)+\left(\dfrac{3}{30}+\dfrac{2}{30}\right)+\left(\dfrac{4}{84}+\dfrac{3}{84}\right)\)
\(=\dfrac{19}{36}+\dfrac{5}{30}+\dfrac{7}{84}\)
\(=\dfrac{19}{36}+\dfrac{1}{6}+\dfrac{1}{12}\)
\(=\dfrac{19}{36}+\dfrac{6}{36}+\dfrac{3}{36}\)
\(=\dfrac{28}{36}=\dfrac{7}{9}\)
Vậy: \(A=\dfrac{7}{9}\)
\(P=\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+\dfrac{1}{28}+\dfrac{1}{36}+\dfrac{1}{45}\)
\(=2\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\right)\)
\(=2\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{10}\right)=2.\dfrac{2}{5}=\dfrac{4}{5}\)
1) So sánh
3 77/379 và 3 79/381
2)
A= 1/6 + 1/10 + 1/15 + 1/21 + 1/28 + 1/36
Giúp mình nhé❤❤❤❤❄▫〰▫▫▫▫▫▫
2) A = \(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}\)
=> \(\frac{1}{2}\).A = \(\frac{1}{2}\).\(\left(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}\right)\)
=> \(\frac{1}{2}\).A = \(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\)
=> \(\frac{1}{2}\).A = \(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\)
=> \(\frac{1}{2}\).A = \(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)
=> \(\frac{1}{2}\).A = \(\frac{1}{3}-\frac{1}{9}\)
=> \(\frac{1}{2}\).A = \(\frac{2}{9}\)
=> A = \(\frac{2}{9}:\frac{1}{2}\)
=> A = \(\frac{4}{9}\)
Coi \(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}\)
\(\Rightarrow\frac{1}{2}A=\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}\right).\frac{1}{2}\)
\(=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{2}-\frac{1}{10}=\frac{2}{5}\)
\(\Rightarrow A=\frac{2}{5}:\frac{1}{2}=\frac{4}{5}\)
\(A=\left(\frac{1}{3}-1\right)\left(\frac{1}{6}-1\right)\left(\frac{1}{10}-1\right)....\left(\frac{1}{36}-1\right)\)
\(=\frac{-2}{3}.\frac{-5}{6}.\frac{-9}{10}...\frac{-35}{36}\)
\(=-\left(\frac{4}{6}.\frac{10}{12}.\frac{18}{20}...\frac{70}{72}\right)=-\left(\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}...\frac{7.10}{8.9}\right)\)
\(=-\left(\frac{1.4.2.5.3.6...7.10}{2.3.3.4.4.5...8.9}\right)=-\frac{\left(1.2.3.4..7\right)\left(4.5.6...10\right)}{\left(2.3.4...8\right)\left(3.4.5...9\right)}=-\frac{1.10}{8.3}=\frac{-10}{24}\)
Đặt biểu thức là A .
Ta có :
\(A=\left(\frac{1}{3}-1\right)\left(\frac{1}{6}-1\right)\left(\frac{1}{10}-1\right)...\left(\frac{1}{36}-1\right)\)
\(A=\frac{-2}{3}\cdot\frac{-5}{6}\cdot\frac{-9}{10}\cdot....\cdot\frac{-36}{36}\)
\(A=-\left(\frac{4}{6}\cdot\frac{10}{12}\cdot\frac{18}{20}\cdot...\cdot\frac{70}{72}\right)\)
\(A=-\left(\frac{1.4}{2.3}\cdot\frac{2.5}{3.4}\cdot\frac{3.6}{4.5}...\frac{7.10}{8.9}\right)\)
\(A=-\left(\frac{1.4.2.5.3.6...7.10}{2.3.3.4.4.5...8.9}\right)\)
\(A=-\frac{\left(1.2.3.4....7\right)\left(4.5.6....10\right)}{\left(2.3.4....8\right)\left(3.4.5....9\right)}\)
\(A=-\frac{1.10}{8.3}\)
\(A=\frac{-10}{24}\)
ta có
(1/3+1/6+1/36) +(1/10+1/15+1/45)+(1/21+1/28)
=(\(\frac{12+6+1}{36}\)+\(\frac{9+6+2}{90}\)+\(\frac{4+3}{84}\)
19/36+17/90+1/12
=(19/36+1/12)+17/90
=7/12+17/90
=105/180+34/180
=139/180
1/3 +1/6+1/10+1/15+1/21+1/28+1/36+1/45
=1/1x3+1/3x2+1/2x5+1/3x5+1/3x7+1/7x4+1/4x9+1/9x5
=1/1-1/3+1/3-1/2....+1/9-1/5
=1/1
\(\frac{1}{2}\) E= \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\)
\(\frac{1}{2}\) E = \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{8.9}\)
\(\frac{1}{2}E\) = \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}\)
\(\frac{1}{2}E\) = \(\frac{1}{2}-\frac{1}{9}\)
\(\frac{1}{2}E\) =\(\frac{7}{18}\)
=> E = \(\frac{7}{9}\)
E=\(\frac{1}{3}+\frac{1}{6}+....+\frac{1}{28}+\frac{1}{36}\)
\(\frac{1}{2}E=\frac{1}{6}+\frac{1}{12}+...+\frac{1}{56}+\frac{1}{72}\)
\(\frac{1}{2}E=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{7.8}+\frac{1}{8.9}\)
\(\frac{1}{2}E=\frac{3-2}{2.3}+\frac{4-3}{3.4}+...\frac{8-7}{7.8}+\frac{9-8}{8.9}\)
\(\frac{1}{2}E=\frac{3}{2.3}-\frac{2}{2.3}+\frac{4}{3.4}-\frac{3}{3.4}+...+\frac{8}{7.8}-\frac{7}{7.8}+\frac{9}{8.9}-\frac{8}{8.9}\)
\(\frac{1}{2}E=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)
\(\frac{1}{2}E=\frac{1}{2}-\frac{1}{9}=\frac{7}{18}\)
E=\(\frac{7}{18}:\frac{1}{2}=\frac{7}{9}\)
đặt A=1/6+1/10+1/15+1/21+1/28+1/36+1/45
A*2=(1/6*+1/10+1/15+1/21+1/28+1/36+1/45)*2
A*2=1/12+1/20+1/30+1/42+1/56+1/72+1/90
A*2=1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10
A*2=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-/8+1/8-1/9+1/9-1/10
A*2=1/3-1/10
A*2=7/30
A=7/30 / 2
A=7/15
A=2(1/2+1/6+...+1/90)
=2(1-1/2+1/2-1/3+...+1/9-1/10)
=2*9/10=9/5<2