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A = \(\dfrac{1}{2}\)+ \(\dfrac{1}{3}\)+ \(\dfrac{1}{4}\)+ \(\dfrac{1}{2}\)+ \(\dfrac{2}{3}\)+ \(\dfrac{3}{4}\)
A = ( \(\dfrac{1}{2}\)+ \(\dfrac{1}{2}\)) + ( \(\dfrac{1}{4}\)+\(\dfrac{3}{4}\)) +( \(\dfrac{1}{3}\)+ \(\dfrac{2}{3}\))
A = 1 + 1 + 1
A = 3
B = ( \(\dfrac{3}{4}\) + \(\dfrac{5}{7}\)+ \(\dfrac{16}{64}\)+ \(\dfrac{2}{7}\)) - 2
B = ( \(\dfrac{3}{4}\)+ \(\dfrac{1}{4}\)) + ( \(\dfrac{5}{7}\)+ \(\dfrac{2}{7}\)) - 2
B = 1 + 1 - 2
B = 2 - 2
B = 0
\(\dfrac{1}{5}+\dfrac{4}{11}+\dfrac{4}{5}+\dfrac{7}{11}=\left(\dfrac{1}{5}+\dfrac{4}{5}\right)+\left(\dfrac{4}{11}+\dfrac{7}{11}\right)=\dfrac{5}{5}+\dfrac{11}{11}=1+1=2\)
\(\dfrac{5}{6}+\dfrac{8}{24}+\dfrac{1}{6}+\dfrac{16}{24}=\dfrac{5}{6}+\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{2}{3}=\left(\dfrac{5}{6}+\dfrac{1}{6}\right)+\left(\dfrac{1}{3}+\dfrac{2}{3}\right)=\dfrac{6}{6}+\dfrac{3}{3}=1+1=2\)
\(\frac{1}{7}+\frac{2}{7}+\frac{3}{7}+\frac{4}{7}+\frac{5}{7}+\frac{6}{7}\)
\(=\left(\frac{1}{7}+\frac{6}{7}\right)+\left(\frac{2}{7}+\frac{5}{7}\right)+\left(\frac{3}{7}+\frac{4}{7}\right)\)
\(=1+1+1=3\)
bn có tíc ko zậy ?
Châu Á là châu lục lớn nhất về diện tích và dân số 4.623.940.078 người (cập nhật 30/01/2020 theo số liệu từ Liên Hợp Quốc), có diện tích khoảng 49.7 triệu km2 chiếm hơn 30% phần đất liền trên trái đất.
\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).\left(1-\frac{1}{5}\right).\left(1-\frac{1}{6}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}\)
\(=\frac{1.2.3.4.5}{2.3.4.5.6}\)
\(=\frac{1}{6}\)
\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\times\left(1-\frac{1}{6}\right)\).
\(=\left(\frac{2}{2}-\frac{1}{2}\right)\times\left(\frac{3}{3}-\frac{1}{3}\right)\times\left(\frac{4}{4}-\frac{1}{4}\right)\times\left(\frac{5}{5}-\frac{1}{5}\right)\times\left(\frac{6}{6}-\frac{1}{6}\right)\).
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{6}\).
\(=\frac{1\times2\times3\times4\times5}{2\times3\times4\times5\times6}=\frac{1}{6}\).
\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{4}{3}+\dfrac{2}{6}+\dfrac{2}{3}+\dfrac{5}{6}\)
\(=\left(\dfrac{1}{3}+\dfrac{4}{3}+\dfrac{2}{3}\right)+\left(\dfrac{1}{6}+\dfrac{2}{6}+\dfrac{5}{6}\right)\)
\(=\dfrac{7}{3}+\dfrac{8}{6}\)\(=\dfrac{7}{3}+\dfrac{4}{3}\)
\(=\dfrac{11}{3}\)
1) Ta có: \(\left(\dfrac{3}{4}\cdot\dfrac{5}{97}+\dfrac{1}{9}\cdot\dfrac{13}{47}\right)\cdot\left(\dfrac{1}{5}-\dfrac{7}{25}\cdot\dfrac{5}{7}\right)\)
\(=\left(\dfrac{3}{4}\cdot\dfrac{5}{97}+\dfrac{1}{9}\cdot\dfrac{13}{47}\right)\cdot\left(\dfrac{1}{5}-\dfrac{1}{5}\right)\)
=0
2) Ta có: \(\dfrac{8}{17}\cdot\dfrac{4}{15}+\dfrac{8}{17}\cdot\dfrac{22}{15}-\dfrac{8}{15}\cdot\dfrac{9}{17}\)
\(=\dfrac{8}{17}\left(\dfrac{4}{15}+\dfrac{22}{15}-\dfrac{9}{15}\right)\)
\(=\dfrac{8}{17}\cdot\dfrac{15}{15}=\dfrac{8}{17}\)
3) Ta có: \(\dfrac{2021}{2}\cdot\dfrac{1}{3}+\dfrac{4042}{4}\cdot\dfrac{1}{5}+\dfrac{6063}{3}\cdot\dfrac{22}{15}\)
\(=\dfrac{2021}{2}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)+2021\cdot\dfrac{22}{15}\)
\(=\dfrac{2021}{2}\cdot\dfrac{8}{15}+\dfrac{2021}{2}\cdot\dfrac{44}{15}\)
\(=\dfrac{2021}{2}\cdot\dfrac{52}{15}\)
\(=\dfrac{52546}{15}\)
4) Ta có: \(\dfrac{4}{7}\cdot\dfrac{2}{13}+\dfrac{8}{13}:\dfrac{7}{4}+\dfrac{4}{7}:\dfrac{13}{2}+\dfrac{4}{7}\cdot\dfrac{1}{13}\)
\(=\dfrac{4}{7}\left(\dfrac{2}{13}+\dfrac{8}{13}+\dfrac{2}{13}+\dfrac{1}{13}\right)\)
\(=\dfrac{4}{7}\)
\(\frac{1}{2}\times\frac{1}{3}+\frac{1}{3}\times\frac{1}{4}+\frac{1}{4}\times\frac{1}{5}+\frac{1}{5}\times\frac{1}{6}\)
\(=\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=\frac{1}{2}-\frac{1}{6}=\frac{2}{6}=\frac{1}{3}\)
\(\frac{1}{2}.\frac{1}{3}+\frac{1}{3}.\frac{1}{4}+\frac{1}{4}.\frac{1}{5}+\frac{1}{5}.\frac{1}{6}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=\frac{1}{2}-\frac{1}{6}\)
\(=\frac{1}{3}\)
1/2 x 1/3 + 1/3 x 1/4 + 1/4 x 1/5 + 1/5 x 1/6
= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6
= 1/2 - 1/6
= 1/3