Question

tìm a biết:

(1-1/3)x(1-1/6)x(1-1/10)x(1-1/15)x...x(1-1/780)xa=1

Answer 1

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

=> \(\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{779}{780}.a=1\)

=> \(\frac{4}{6}.\frac{10}{12}.\frac{18}{20}.\frac{28}{30}...\frac{1558}{1560}.a=1\)

=> \(\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}.\frac{4.7}{5.6}...\frac{38.41}{39.40}.a=1\)

=> \(\frac{1.2.3.4...38}{2.3.4.5...39}.\frac{4.5.6.7...41}{3.4.5.6...40}.a=1\)

=> \(\frac{1}{39}.\frac{41}{3}.a=1\)

=> \(\frac{41}{117}.a=1\)

=> \(a=1:\frac{41}{117}=\frac{117}{41}\)

Answer 2

117/41

Answer 3

4949/19800