Question

\(1\frac{1}{3}x1\frac{1}{8}x1\frac{1}{15}x..........x1\frac{1}{9800}\)

Answer 1

#)Giải :

\(1\frac{1}{3}\times1\frac{1}{8}\times1\frac{1}{15}\times...\times1\frac{1}{9800}\)

\(=\frac{4}{3}\times\frac{9}{8}\times\frac{16}{15}\times...\times\frac{9801}{9800}\)

\(=\frac{2.2}{1.3}\times\frac{3.3}{2.4}\times\frac{4.4}{3.5}\times...\times\frac{99.99}{98.100}\)

\(=\frac{2.3.4.....99}{1.2.3.....98}\times\frac{2.3.4.....99}{3.4.5.....100}\)

\(=99\times\frac{2}{100}=\frac{198}{100}=\frac{99}{50}\)

Answer 2

\(=\frac{4}{3}\times\frac{9}{8}\times\frac{16}{15}\times...\times\frac{9801}{9800}\)

\(=\frac{2.2}{1.3}\times\frac{3.3}{2.4}\times\frac{4.4}{3.5}\times...\times\frac{99.99}{98.100}\)

\(=\frac{2.3.4.5.....99}{1.2.3.4....98}\times\frac{2.3.4.5.....99}{3.4.5.6.....100}\)

\(=\frac{99}{1}\times\frac{2}{100}\)

\(=\frac{99}{50}\)

Answer 3

\(1\frac{1}{3}\times1\frac{1}{8}\times1\frac{1}{15}\times........\times1\frac{1}{9800}\)

\(=\frac{4}{3}\times\frac{9}{8}\times\frac{16}{15}\times.......\times\frac{9801}{9800}\)

\(=\frac{2\times2}{1\times3}\times\frac{3\times3}{2\times4}\times\frac{4\times4}{3\times5}\times......\times\frac{99\times99}{98\times100}\)

\(=2\times\left(\frac{2}{3}\times\frac{3}{2}\times\frac{3}{4}\times\frac{4}{3}\times.....\times\frac{99}{98}\times\frac{99}{100}\right)\)

\(=2\times\frac{99}{100}\)

\(=\frac{198}{100}=\frac{99}{50}\)