Question

Tính: A= \(\left(1-\dfrac{1}{15}\right)\left(1-\dfrac{1}{21}\right)\left(1-\dfrac{1}{28}\right)...\left(1-\dfrac{1}{210}\right)\)

Answer 1

\(A=\left(1-\dfrac{1}{15}\right).\left(1-\dfrac{1}{21}\right).\left(1-\dfrac{1}{28}\right)....\left(1-\dfrac{1}{210}\right)\)

\(A=\dfrac{14}{15}.\dfrac{20}{21}.\dfrac{27}{28}....\dfrac{209}{210}\)

\(A=\dfrac{14.2}{15.2}.\dfrac{20.2}{21.2}.\dfrac{27.2}{28.2}....\dfrac{209.2}{210.2}\)

\(A=\dfrac{4.7}{5.6}.\dfrac{5.8}{6.7}.\dfrac{6.9}{7.8}....\dfrac{19.22}{20.21}\)

\(A=\dfrac{4.5.6....19}{5.6.7....20}.\dfrac{7.8.9....22}{6.7.8....21}\)

\(A=\dfrac{4}{20}.\dfrac{22}{6}\)

\(A=\dfrac{11}{15}\)