a) \(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times...\times\left(1-\frac{1}{18}\right)\times\left(1-\frac{1}{19}\right)\times\left(1-\frac{1}{20}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{17}{18}\times\frac{18}{19}\times\frac{19}{20}\)
\(=\frac{1}{20}\)
b)\(1\frac{1}{2}\times1\frac{1}{3}\times1\frac{1}{4}\times...\times1\frac{1}{2005}\times1\frac{1}{2006}\times1\frac{1}{2007}\)
\(=\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times...\times\frac{2006}{2005}\times\frac{2007}{2006}\times\frac{2008}{2007}\)
\(=\frac{2008}{2}\)
\(=1004\)
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