Question

1\(\frac{1}{3}\)x 1\(\frac{1}{8}\)x 1\(\frac{1}{15}\)x1 \(\frac{1}{24}\)x .....x 1\(\frac{1}{99}\)

Answer 1

\(=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.\frac{25}{24}...\frac{100}{99}\)

Answer 2

\(1\frac{1}{3}\times1\frac{1}{8}\times1\frac{1}{15}\times1\frac{1}{24}\times...\times1\frac{1}{99}\)

\(=\frac{4}{3}\times\frac{9}{8}\times\frac{16}{15}\times\frac{25}{24}\times...\times\frac{100}{99}\)

\(=\frac{2\times2}{1\times3}\times\frac{3\times3}{2\times4}\times\frac{4\times4}{3\times5}\times\frac{5\times5}{4\times6}\times...\times\frac{10\times10}{9\times11}\)

\(=\frac{2}{1}\times\frac{10}{11}\)

\(=\frac{20}{11}\)