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\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}+\frac{1}{486}\)
\(3\times A=\frac{3}{2}+\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}\)
\(3\times A-A=\left(\frac{3}{2}+\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}\right)-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\frac{1}{54}+\frac{1}{162}+\frac{1}{486}\right)\)
\(2\times A=\frac{3}{2}-\frac{1}{486}\)
\(A=\frac{182}{243}\)
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a, 42x(54+17):71
=42x71:71=42
b, 123x(154-65):89
=123x89:89=123
c,324x(6+4):324
=324x10:324=10x324:324=10
\(a)\left(42\times54+17\times42\right):71\)
\(=42\times54+17\times42:71\)
\(=42\times\left(54+17\right):71\)
\(=42\times71:71\)
\(=42\)
\(b)\left(123\times154-65\times123\right):89\)
\(=123\times154-65\times123:89\)
\(=123\times\left(154-65\right):89\)
\(=123\times89:89\)
\(=123\)
\(c)\left(324\times6+4\times324\right):\left(162\times2\right)\)
\(=324\times6+4\times324:324\)
\(=324\times\left(6+4\right):324\)
\(=324\times10:324\)
\(=3240:324\)
\(=10\)
=36 x 1652 + 64 x 1652
=1652 x (36+64)
=1652 x 100
=165200
64 x 8 + 48 x 4 + 6 x16
= 64 x2 x4 + 48 x 4 + 6 x 4 x 4
= 128 x 4 + 48 x4 + 24 x 4
= ( 128 + 48 + 24 ) x 4
= 200 x 4
= 800
= 35*(20,10-19,45)+65*(20,10-19,45)
=35*0,65+65*0,65
=0,65*(35+65)
=0,65*100
=65
64 x 867 + 867 x 36 - 30 x 867
= 867 (64 + 36 - 30)
= 867 * 70
= 60690
\(\frac{37}{35}:\frac{5}{4}:\frac{74}{25}\)
\(=\frac{37}{35}:\left(\frac{5}{4}\times\frac{74}{25}\right)\)
\(=\frac{37}{35}:\frac{37}{10}\)
\(=\frac{2}{7}\)
\(\frac{37}{35}:\frac{5}{4}:\frac{74}{25}\)
=\(\frac{37}{35}x\frac{4}{5}x\frac{25}{74}\)
\(=\left(\frac{37}{35}x\frac{25}{74}\right)x\frac{4}{5}\)
\(=\frac{1}{7}x\frac{5}{2}x\frac{4}{5}\)
\(=\frac{1x5x2x2}{7x2x5}\)
\(=\frac{2}{7}\)
35*64+162*162+162
=35*64+162*162+162*1
=35*64+162*(162+1)
=35*64+162*163
=2240+26406
=28646