Question

 Tinh

(1 - 1/3) * (1 - 1/6) * ... * (1 - 1/210)

Answer 1

A = \(\frac{2}{3}\). \(\frac{5}{6}\). \(\frac{9}{10}\).\(\frac{14}{15}\)... \(\frac{209}{210}\)

  = \(\frac{4}{6}\). \(\frac{10}{12}\).\(\frac{18}{20}\).\(\frac{28}{30}\)... \(\frac{418}{420}\)

  = \(\frac{4.10.18.28...418}{6.12.20.30...420}\)

  =  \(\frac{1.4.2.5.3.6.4.7...19.22}{2.3.3.4.4.5.5.6...20.21}\)

  = \(\frac{\left(1.2.3.4...19\right)\left(4.5.6.7...22\right)}{\left(2.3.4.5...20\right)\left(3.4.5.6...21\right)}\)

  =  \(\frac{1.22}{20.3}\)= \(\frac{22}{60}\)= \(\frac{11}{30}\)