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计算：
(1) $\frac{1}{2} × \frac{2}{3} × \frac{3}{4} × \dots × \frac{49}{50}$；
(2) $(1 - \frac{1}{2}) × (1 + \frac{1}{2}) × (1 - \frac{1}{3}) × (1 + \frac{1}{3}) × (1 - \frac{1}{4}) × (1 + \frac{1}{4})$；
(3) $(\frac{1}{2} × \frac{3}{2}) × (\frac{2}{3} × \frac{4}{3}) × \dots × (\frac{2012}{2013} × \frac{2014}{2013}) × (\frac{2013}{2014} × \frac{2015}{2014})$；
(4) $(1 - \frac{1}{100}) × (1 - \frac{1}{99}) × (1 - \frac{1}{98}) × \dots × (1 - \frac{1}{3}) × (1 - \frac{1}{2})$；
(5) $(1 + \frac{1}{2}) × (1 + \frac{1}{4}) × (1 + \frac{1}{6}) × \dots × (1 + \frac{1}{20}) × (1 - \frac{1}{3}) × (1 - \frac{1}{5}) × (1 - \frac{1}{7}) × \dots × (1 - \frac{1}{21})$。
(1) $\frac{1}{2} × \frac{2}{3} × \frac{3}{4} × \dots × \frac{49}{50}$；
(2) $(1 - \frac{1}{2}) × (1 + \frac{1}{2}) × (1 - \frac{1}{3}) × (1 + \frac{1}{3}) × (1 - \frac{1}{4}) × (1 + \frac{1}{4})$；
(3) $(\frac{1}{2} × \frac{3}{2}) × (\frac{2}{3} × \frac{4}{3}) × \dots × (\frac{2012}{2013} × \frac{2014}{2013}) × (\frac{2013}{2014} × \frac{2015}{2014})$；
(4) $(1 - \frac{1}{100}) × (1 - \frac{1}{99}) × (1 - \frac{1}{98}) × \dots × (1 - \frac{1}{3}) × (1 - \frac{1}{2})$；
(5) $(1 + \frac{1}{2}) × (1 + \frac{1}{4}) × (1 + \frac{1}{6}) × \dots × (1 + \frac{1}{20}) × (1 - \frac{1}{3}) × (1 - \frac{1}{5}) × (1 - \frac{1}{7}) × \dots × (1 - \frac{1}{21})$。
答案
(1) $\dfrac{1}{50}$
(2) $\dfrac{5}{8}$
【解析】原式$=\dfrac{1}{2}×\dfrac{3}{2}×\dfrac{2}{3}×\dfrac{4}{3}×\dfrac{3}{4}×\dfrac{5}{4}=\dfrac{5}{8}.$
(3) $\dfrac{2\ 015}{4\ 028}$
(4) $\dfrac{1}{100}$
(5) $1$
(2) $\dfrac{5}{8}$
【解析】原式$=\dfrac{1}{2}×\dfrac{3}{2}×\dfrac{2}{3}×\dfrac{4}{3}×\dfrac{3}{4}×\dfrac{5}{4}=\dfrac{5}{8}.$
(3) $\dfrac{2\ 015}{4\ 028}$
(4) $\dfrac{1}{100}$
(5) $1$
