Question

(1-1/2)x(1-1/3)x(1-1/4)x...x(1-1/2004)

Answer 1

Đặt \(A=\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{2004}\right)\)

\(A=\left(\dfrac{2}{2}-\dfrac{1}{2}\right).\left(\dfrac{3}{3}-\dfrac{1}{3}\right)....\left(\dfrac{2003}{2003}-\dfrac{1}{2003}\right).\left(\dfrac{2004}{2004}-\dfrac{1}{2004}\right)\)

\(A=\dfrac{1}{2}.\dfrac{2}{3}...\dfrac{2002}{2003}.\dfrac{2003}{2004}\)

\(A=\dfrac{1.2.3...2002.2003}{2.3....2003.2004}\)

\(A=\dfrac{1}{2004}\)

Answer 2

\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)..............\left(1-\dfrac{1}{2004}\right)\)

\(=\left(\dfrac{2}{2}-\dfrac{1}{2}\right)\left(\dfrac{3}{3}-\dfrac{1}{3}\right)...........\left(\dfrac{2004}{2004}-\dfrac{1}{2004}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.............\dfrac{2003}{2004}\)

\(=\dfrac{1}{2004}\)

Answer 3

\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{2004}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.....\dfrac{2003}{2004}\)

\(=\dfrac{1.2.3....2003}{2.3.4....2004}\)

\(=\dfrac{1}{2004}\)