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(1-1/3)x(1-1/5)x(1-1/7)x(1-1/9)x(1-1/2)x(1-1/4)x(1-1/6)x(1-1/8)x(1-1/10)
=2/3x4/5x6/7x8/9x1/2x3/4x5/6x7/8x9/10
=2x4x6x8x1x3x5x7x9 /3x5x7x9x2x4x6x8x10
=1/10
\(A=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)..............\left(1-\frac{1}{780}\right)\)
\(A=\frac{2}{3}.\frac{5}{6}.......\frac{779}{780}\)
\(A=\frac{4}{6}.\frac{10}{12}........\frac{1558}{1560}\)
\(A=\frac{1.4.2.5...........38.41}{2.3.3.4..........39.40}\)
\(A=\frac{\left(1.2.......38\right).\left(4.5..........41\right)}{\left(2.3.......39\right).\left(3.4............40\right)}\)
\(A=\frac{41}{39}\)
\(A=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right).......\left(1-\frac{1}{780}\right)\)
\(=\left(\frac{3}{3}-\frac{1}{3}\right)\left(\frac{6}{6}-\frac{1}{6}\right)..........\left(\frac{780}{780}-\frac{1}{780}\right)\)
\(=\frac{2}{3}.\frac{5}{6}..............\frac{779}{780}\)
sao nữa??