Question

B = \(\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).......\left(1-\dfrac{1}{20}\right)\)

Answer 1

Ta có :

\(B=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)..............\left(1-\dfrac{1}{20}\right)\)

\(B=\left(\dfrac{2}{2}-\dfrac{1}{2}\right)\left(\dfrac{3}{3}-\dfrac{1}{3}\right)...............\left(\dfrac{20}{20}-\dfrac{1}{20}\right)\)

\(B=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}............\dfrac{19}{20}\)

\(B=\dfrac{1.2.3...........19}{2.3.4..........19.20}\)\(=\dfrac{1}{20}\)

Answer 2

\(B=\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).....\left(1-\dfrac{1}{20}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.....\dfrac{19}{20}\)

\(=\dfrac{1}{20}\)