Question

Tính giá trị các biểu thức:

\(\left(1-\frac{1}{3}\right).\left(1-\frac{1}{6}\right)\) \(.\left(1-\frac{1}{10}\right).\left(1-\frac{1}{15}\right)\) \(.....\left(1-\frac{1}{780}\right)\)

Answer 1

\(A=\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{6}\right).\left(1-\dfrac{1}{10}\right)...\left(1-\dfrac{1}{780}\right)\\ =\dfrac{2}{3}.\dfrac{5}{6}.\dfrac{9}{10}...\dfrac{779}{780}\\ =\dfrac{4}{6}.\dfrac{10}{12}.\dfrac{18}{20}...\dfrac{1558}{1560}\\ =\dfrac{1.4}{2.3}.\dfrac{2.5}{3.4}.\dfrac{3.6}{4.5}...\dfrac{38.41}{39.40}=\dfrac{1.2.3..38}{2.3...39}.\dfrac{4.5...41}{3.4...40}\\ =\dfrac{1}{39}.\dfrac{41}{3}=\dfrac{41}{117}\)