\(G=\left(\frac{1}{3}-1\right)\left(\frac{1}{6}-1\right)\left(\frac{1}{15}-1\right)\left(\frac{1}{21}-1\right)\left(\frac{1}{36}-1\right)\)
Tính G
K
Khách
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S
20 tháng 1 2018
\(=\frac{-2}{3}\cdot\frac{-5}{6}\cdot\frac{-9}{10}\cdot\cdot\cdot\cdot\frac{-35}{36}\)
\(=\frac{-4}{6}\cdot\frac{-10}{12}\cdot\frac{-18}{20}\cdot\cdot\cdot\cdot\frac{-70}{72}\)
\(=\frac{-1.4}{2.3}\cdot\frac{-2.5}{3.4}\cdot\frac{-3.6}{4.5}\cdot\cdot\cdot\cdot\frac{-7.10}{8.9}\)
\(=\frac{\left(-1\right).\left(-2\right).\left(-3\right)...\left(-7\right)}{2.3.4....8}\cdot\frac{4.5.6....10}{3.4.5....9}\)
\(=\frac{\left(-1\right).2.3...7}{2.3.4....8}\cdot\frac{10}{3}\)
\(=\frac{-1}{8}\cdot\frac{10}{3}=\frac{-5}{12}\)
3 tháng 6 2016
A = ( 1/3 - 1).( 1/6 - 1).( 1/10 - 1).( 1/15 - 1).( 1/21 - 1).( 1/28 - 1).( 1/36 - 1)
A = -2/3 . ( -5/6) . ( -9/10) . ( -14/15) . ( -20/21) . ( -27/28) . ( -35/36)
Do tích A có lẻ thừa số, mỗi thừa số đều mang dấu âm nên A mang dấu âm
A = -[ 2/3 . 5/6 . 9/10 . 14/15 . 20/21 . 27/28 . 35/36]
Đặt B = 2/3 . 5/6 . 9/10 . 14/15 . 20/21 . 27/28 . 35/36
B = 4/6 . 10/12 . 18/20 . 28/30 . 40/42 . 54/56 . 70/72
B = 1.4/2.3 . 2.5/3.4 . 3.6/4.5 . 4.7/5.6 . 5.8/6.7 . 6.9/7.8 . 7.10/8.9
B = 1.2.3.4.5.6.7/3.4.5.6.7.8.9 . 4.5.6.7.8.9.10/2.3.4.5.6.7.8
B = 2/8.9 . 9.10/2.3
B = 5/12
A = -5/12
3 tháng 4 2019
=2/3.5/6.9/10.14/15.20/21.27/28
=5/9.21/15.45/49
=7/9.45/49
=5/7
hơi dài dòng nhưng mong bạn tích đúng cho mk nha
13 tháng 8 2017
\(\left(1-\frac{1}{3}\right)\)\(x\left(1-\frac{1}{6}\right)\)\(x\)\(\left(1-\frac{1}{10}\right)\)\(x\)\(\left(1-\frac{1}{15}\right)\)\(x\)\(\left(1-\frac{1}{21}\right)\)\(x\)\(\left(1-\frac{1}{28}\right)\)\(=\)\(\left(\frac{3}{3}-\frac{1}{3}\right)\)\(x\)\(\left(\frac{6}{6}-\frac{1}{6}\right)\)\(x\)\(\left(\frac{10}{10}-\frac{1}{10}\right)\)\(x\)\(\left(\frac{15}{15}-\frac{1}{15}\right)\)\(x\)\(\left(\frac{21}{21}-\frac{1}{21}\right)\)\(x\)\(\left(\frac{28}{28}-\frac{1}{28}\right)\)\(=\)\(\frac{2}{3}x\frac{5}{6}x\frac{9}{10}x\frac{14}{15}x\frac{20}{21}x\frac{27}{28}\)\(=\)\(\frac{2x5x9x14x20x27}{3x6x10x15x21x28}\)\(=\)\(\frac{2x5\left(3x3\right)x\left(2x7\right)x\left(5x4\right)x\left(3x3x3\right)}{3x\left(3x2\right)x\left(5x2\right)x\left(5x3\right)x\left(7x3\right)x\left(4x7\right)}\)\(=\)\(\frac{3}{7}\)
\(G=\left(\frac{1}{3}-1\right)\left(\frac{1}{6}-1\right)\left(\frac{1}{15}-1\right)\left(\frac{1}{21}-1\right)\left(\frac{1}{36}-1\right)\)
\(\Leftrightarrow G=-\frac{2}{3}.\frac{-5}{6}.\frac{-14}{15}.\frac{-20}{21}.\frac{-35}{36}\)
\(\Leftrightarrow G=\frac{-2.}{3}.\frac{5}{6}.\frac{14}{15}.\frac{20}{21}.\frac{35}{36}\)
\(\Leftrightarrow G=\frac{-2.5.2.7.2.2.5.5.7}{3.2.3.3.5.3.7.2.3.2.3}\)
\(\Leftrightarrow G=\frac{-2^4.5^3.7^2}{2^3.3^6.5.7}\)
\(\Leftrightarrow G=\frac{-2.5^2.7}{3^6}\)
\(\Leftrightarrow G=\frac{-350}{729}\)
P/s : Xin lỗi vì cách giải cùi bắp của mình :((