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T = 3/4 x 8/9 x 15/16 x ... x 575/576 x 624/625
T = (1x3/1x4) x (2x4/3x3) x (3x5/4x4) x ... x (23x25/24x24) x (24x26/25x25)
T = [1 x 2/3 x 3/4 x 4/5 x ... x 23/24 x 24/25] x [3/5 x 4/3 x 5/4 x 6/5 x ... x 25/24 x 26/25]
T = 2/25 x 26/5
T = 52/125
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\(\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{9}\right)x\left(1-\frac{1}{16}\right)x...x\left(1-\frac{1}{576}\right)x\left(1-\frac{1}{625}\right)\)
\(=\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x...x\frac{575}{576}x\frac{624}{625}=\frac{1x3}{1x4}x\frac{2x4}{3x3}x\frac{3x5}{4x4}x...x\frac{23x25}{24x24}x\frac{24x26}{25x25}\)
\(=\left(\frac{1}{1}x\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x...x\frac{23}{24}x\frac{24}{25}=\frac{1x2x3x4x...x23x24}{1x3x4x5x...x24x25}=\frac{2}{25}\right)\left(\frac{3}{5}x\frac{4}{3}x\frac{5}{4}x\frac{6}{5}x...x\frac{25}{24}x\frac{26}{25}=\frac{3x4x5x6x...x25x26}{5x3x4x5x...x24x25}=\frac{26}{5}\right)\)
\(\frac{2}{25}x\frac{26}{5}=\frac{52}{50}=\frac{26}{25}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đây là toán lớp 5 hay lớp 6 vậy.
Nếu đây là toán 6 thì tớ giải cho.