Question

tính : ( 1-1/3^2 ) . (1-1/4^2 ) . ( 1-1/5^2) .(1-1/6^2).(1-1/7^2).(1-1/8^2)

Answer 1

\(A=\left(1-\dfrac{1}{3^2}\right).\left(1-\dfrac{1}{4^2}\right)\left(1-\dfrac{1}{5^2}\right).....\left(1-\dfrac{1}{8^2}\right)\)

\(A=\left[\left(1-\dfrac{1}{3}\right)\left(1+\dfrac{1}{3}\right)\right].\left[\left(1-\dfrac{1}{4}\right)\left(1+\dfrac{1}{4}\right)\right].........\left[\left(1-\dfrac{1}{8}\right)\left(1+\dfrac{1}{8}\right)\right]\)\(A=\left[\dfrac{2}{3}.\dfrac{4}{3}\right].\left[\dfrac{3}{4}.\dfrac{5}{4}\right].........\left[\dfrac{7}{8}.\dfrac{9}{8}\right]\)

\(A=\dfrac{2.3.4.5.6.7}{3.4.5.6.7.8}.\dfrac{4.5.6.7.8.9}{3.4.5.6.7.8}=\dfrac{2}{8}.\dfrac{9}{3}=\dfrac{1}{4}.\dfrac{3}{1}=\dfrac{3}{4}\)