Question

Tính : 

A= (1- \(\dfrac{1}{2}\)) .(1- \(\dfrac{1}{3}\)). ( 1- \(\dfrac{1}{4}\)) . ... . (1 - \(\dfrac{1}{30}\))

B= 1\(\dfrac{1}{3}\) . 1\(\dfrac{1}{8}\) . 1\(\dfrac{1}{15}\) . 1\(\dfrac{1}{24}\) . ... . 1\(\dfrac{1}{168}\)

Answer 1

\(A=\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{30}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}...\dfrac{29}{30}\)

\(=\dfrac{1.2.3...29}{2.3.4...30}\)

\(=\dfrac{1}{30}\)

\(B=1\dfrac{1}{3}.1\dfrac{1}{8}.1\dfrac{1}{15}.1\dfrac{1}{24}...1\dfrac{1}{168}\)

\(=\dfrac{4}{3}.\dfrac{9}{8}.\dfrac{16}{15}.\dfrac{25}{24}...\dfrac{169}{168}\)

\(=\dfrac{4.9.16.25...169}{3.8.15.24...168}\)

\(=\dfrac{2.3.4...13}{1.2.3...12}.\dfrac{2.3.4...13}{3.4.5...14}\)

\(=13.\dfrac{1}{7}\)

\(=\dfrac{13}{7}\).

Answer 2

A = \(\dfrac{1}{2}x\dfrac{2}{3}x\dfrac{3}{4}x...x\dfrac{29}{30}=1x1x1x...x\dfrac{1}{30}=\dfrac{1}{30}\)

B = \(\dfrac{4}{3}x\dfrac{9}{8}x\dfrac{16}{15}x\dfrac{25}{24}x...x\dfrac{169}{168}=1x1x1x1x...x\dfrac{13}{7}=\dfrac{13}{7}\)

Câu B em chưa rõ cách làm nhanh cho lắm. Nếu ko cần tính nhanh thì chị có thể giải bình thường ra giấy ha.