Question

tinh t=(1-1/4)*(1-1/9)*(1-1/16)*...*(1-1/576)*(1-1/625)

Answer 1

 

\(\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{9}\right)x\left(1-\frac{1}{16}\right)x...x\left(1-\frac{1}{576}\right)x\left(1-\frac{1}{625}\right)\)

 

\(=\frac{3}{4}x\frac{8}{9}x\frac{15}{16}x...x\frac{575}{576}x\frac{624}{625}=\frac{1x3}{1x4}x\frac{2x4}{3x3}x\frac{3x5}{4x4}x...x\frac{23x25}{24x24}x\frac{24x26}{25x25}\)

\(=\left(\frac{1}{1}x\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x...x\frac{23}{24}x\frac{24}{25}=\frac{1x2x3x4x...x23x24}{1x3x4x5x...x24x25}=\frac{2}{25}\right)\left(\frac{3}{5}x\frac{4}{3}x\frac{5}{4}x\frac{6}{5}x...x\frac{25}{24}x\frac{26}{25}=\frac{3x4x5x6x...x25x26}{5x3x4x5x...x24x25}=\frac{26}{5}\right)\)

 

\(\frac{2}{25}x\frac{26}{5}=\frac{52}{50}=\frac{26}{25}\)

Answer 2

nguyễn như đạt sai rồi kết quả phải là 13/25 mk làm rùi 

Answer 3

ket qua =13/25 do dat a

Answer 4

cho mình hỏi từ phép tính 3 trở xuống thì (3/5*4/3*5/4*6/5*.....*25/24*26/25) ở đâu ra vậy bạn?

Answer 5

13/25