Question

Tìm D. Ai làm đc lời giải phép tính đầy đủ mình tick cho

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

Answer 1

D = $\frac{2}{3}.\frac{5}{6}.\frac{9}{10}. ... .\frac{799}{780}$

   = $\frac{2.2}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}. ... .\frac{38.41}{39.40}$

   = $\frac{2.2}{2.3}.\frac{2.3. ... .38}{3.4. ... 39}.\frac{5.6. ... .41}{4.5. ... .40}$

   = $\frac{2}{3}.\frac{2}{39}.\frac{41}{4}$

   = $\frac{41}{3.39}$

Answer 2

D = \(\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}.....\frac{779}{780}\)

   = \(\frac{2.2}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}.\frac{4.7}{5.6}.....\frac{38.41}{39.40}\)

   = \(\frac{2}{3}.\frac{2.3.4....38}{3.4.5....39}.\frac{5.6.7.....41}{4.5.6.....40}\)

   = \(\frac{2}{3}.\frac{2}{39}.\frac{41}{4}\)

   = \(\frac{41}{117}\)