Question

[Lê Thanh Mai]

1 1/3 * 1 1/8 * 1 1/24 *...* 1 1/99

Answer 1

[Lê Minh Vũ]

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

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

\(=\)\(\frac{\left(2.2\right).\left(3.3\right).\left(4.4\right).\left(5.5\right).....\left(10.10\right)}{\left(1.3\right).\left(2.4\right).\left(3.5\right).\left(4.6\right).....\left(9.11\right)}\)

\(=\)\(\frac{\left(2.3.4.5.....10\right).\left(2.3.4.5.....10\right)}{\left(1.2.3.4.....9\right).\left(3.4.5.....11\right)}\)

\(=\)\(10.\frac{2}{11}\)

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