Tính tổng: $A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{2\,014.2\,015}$.

Tính tổng $S=\dfrac{1}{9.10}+\dfrac{1}{10.11}+...+\dfrac{1}{2\,004.2\,005}$.

Tính tổng $S=1-\dfrac{11}{6}+\dfrac{19}{12}-\dfrac{29}{20}+\dfrac{41}{30}-\dfrac{55}{42}+\dfrac{71}{56}-\dfrac{89}{72}+\dfrac{109}{90}$.