Question

Tính nhanh:

C=( \(\frac{7}{9}\)+ 1)( \(\frac{7}{20}\)+ 1)( \(\frac{7}{33}\)+ 1).....( \(\frac{7}{10800}\)+ 1).

Answer 1

\(C=\left(\frac{7}{9}+1\right)\left(\frac{7}{20}+1\right)\left(\frac{7}{33}+1\right)...\left(\frac{7}{10800}+1\right)\)

\(=\frac{16}{9}.\frac{27}{20}.\frac{40}{33}.....\frac{10807}{10800}\)

\(=\frac{2.8}{1.9}.\frac{3.9}{2.10}.\frac{4.10}{3.11}.....\frac{101.107}{100.108}\)

\(=\frac{2.3.4....101}{1.2.3....100}.\frac{8.9.10...107}{9.10.11...108}\)

\(=101.\frac{2}{27}\)\(=\frac{202}{27}\)