Question

Tính nhanh:

\(1\frac{1}{5}\)x\(1\frac{1}{6}\)x\(1\frac{1}{7}\)x.........x\(1\frac{1}{1998}\)x\(1\frac{1}{1999}\)

Answer 1

\(1\frac{1}{5}\cdot1\frac{1}{6}\cdot1\frac{1}{7}\cdot...\cdot1\frac{1}{1998}\cdot1\frac{1}{1999}\)

\(=\frac{6}{5}\cdot\frac{7}{6}\cdot\frac{8}{7}\cdot...\cdot\frac{1999}{1998}\cdot\frac{2000}{1999}\)

\(=\frac{6\cdot7\cdot8\cdot...\cdot1999\cdot2000}{5\cdot6\cdot7\cdot...\cdot1998\cdot1999}\)

\(=\frac{2000}{5}=400\)

Answer 2

\(1\frac{1}{5}‧1\frac{1}{6}‧1\frac{1}{7}‧.......‧1\frac{1}{1998}‧1\frac{1}{1999}\)

\(=\frac{6}{5}‧\frac{7}{6}\frac{8}{7}‧.......‧\frac{1999}{1998}‧\frac{2000}{1999}\)

\(=\frac{6‧7‧8‧.......‧1999‧2000}{5‧6‧7‧.......‧1998‧1999}\)

\(=400\)

Answer 3

\(1\frac{1}{5}\cdot1\frac{1}{6}\cdot1\frac{1}{7}\cdot...\cdot1\frac{1}{1998}\cdot1\frac{1}{1999}\)

\(=\frac{6}{5}\cdot\frac{7}{6}\cdot\frac{8}{7}\cdot...\cdot\frac{1999}{1998}\cdot\frac{2000}{1999}\)

\(=\frac{6\cdot7\cdot8\cdot...8\cdot1999\cdot2000}{5\cdot6\cdot7\cdot...\cdot1998\cdot1999}\)

\(=\frac{2000}{5}=400\)