\(\dfrac{3}{4.7}+\dfrac{4}{7.11}+\dfrac{5}{11.16}+...+\dfrac{14}{92.106}\)
= \(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+...+\dfrac{1}{92}-\dfrac{1}{106}\)
= \(\dfrac{1}{4}-\dfrac{1}{106}\)
= \(\dfrac{51}{212}\)

\(\dfrac{12}{1.5}+\dfrac{12}{5.9}+...+\dfrac{12}{93.97}+\dfrac{12}{97.101}\)
= \(3.\left(\dfrac{4}{1.5}+\dfrac{4}{5.9}+...+\dfrac{4}{93.97}+\dfrac{4}{97.101}\right)\)
= \(3.\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{93}-\dfrac{1}{97}+\dfrac{1}{97}-\dfrac{1}{101}\right)\)
= \(3.\left(1-\dfrac{1}{101}\right)\)
= \(3.\dfrac{100}{101}\)
= \(\dfrac{300}{101}=2\dfrac{98}{101}\)

x là số tự nhiên hay số nguyên.