3. Вычислите: \(1\frac{2}{11}\cdot 1\frac{2}{13}\cdot 1\frac{2}{15}\cdot 1\frac{2}{17}\cdot 1\frac{2}{19}\cdot 1\frac{2}{21}.\)

Преобразуем смешанные дроби в неправильные:

\(1\frac{2}{11} = \frac{1 \cdot 11 + 2}{11} = \frac{11 + 2}{11} = \frac{13}{11}\)

\(1\frac{2}{13} = \frac{1 \cdot 13 + 2}{13} = \frac{13 + 2}{13} = \frac{15}{13}\)

\(1\frac{2}{15} = \frac{1 \cdot 15 + 2}{15} = \frac{15 + 2}{15} = \frac{17}{15}\)

\(1\frac{2}{17} = \frac{1 \cdot 17 + 2}{17} = \frac{17 + 2}{17} = \frac{19}{17}\)

\(1\frac{2}{19} = \frac{1 \cdot 19 + 2}{19} = \frac{19 + 2}{19} = \frac{21}{19}\)

\(1\frac{2}{21} = \frac{1 \cdot 21 + 2}{21} = \frac{21 + 2}{21} = \frac{23}{21}\)

Выполним умножение:

\(\frac{13}{11} \cdot \frac{15}{13} \cdot \frac{17}{15} \cdot \frac{19}{17} \cdot \frac{21}{19} \cdot \frac{23}{21} = \frac{13 \cdot 15 \cdot 17 \cdot 19 \cdot 21 \cdot 23}{11 \cdot 13 \cdot 15 \cdot 17 \cdot 19 \cdot 21} = \frac{23}{11}\)

Выделим целую часть:

\(\frac{23}{11} = 2\frac{1}{11}\)

Ответ: \(2\frac{1}{11}\)