Question

[Jenny phạm]

a) A = \(\left(1-\frac{1}{2}\right)\). \(\left(1-\frac{1}{3}\right)\). \(\left(1-\frac{1}{4}\right)\). . . . . \(\left(1-\frac{1}{1000}\right)\)

b) B =\(\left(1-\frac{1}{5}\right)\) \(\left(1-\frac{2}{5}\right)\). \(\left(1-\frac{3}{5}\right)\). . . . .  \(\left(1-\frac{2005}{5}\right)\)

c) C = \(\frac{8}{9}\). \(\frac{15}{16}\). \(\frac{24}{25}\). . . . . \(\frac{2499}{2500}\)

d) D= \(\left(1-\frac{1}{3}\right)\). \(\left(1-\frac{1}{6}\right)\). \(\left(1-\frac{1}{10}\right)\). . . . . \(\left(1-\frac{1}{780}\right)\)

Answer 1

[mi ni on s]

\(C=\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.........\frac{2499}{2500}\)

\(=\frac{2.4}{3^2}.\frac{3.5}{4^2}.\frac{4.6}{5^2}......\frac{49.51}{50^2}\)

\(=\frac{2.3.4....49}{3.4.5....50}.\frac{4.5.6....51}{3.4.5....50}\)

\(=\frac{1}{25}.17=\frac{17}{25}\)

Answer 2

[Phùng Minh Quân]

\(a)\) \(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{1000}\right)\)

\(A=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{999}{1000}\)

\(A=\frac{1.2.3.....999}{2.3.4.....1000}\)

\(A=\frac{1}{1000}.\frac{2.3.4.....999}{2.3.4.....999}\)

\(A=\frac{1}{1000}\)

Vậy \(A=\frac{1}{1000}\)