\(s=\)\(\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+...+\dfrac{1}{9\cdot11}\)
=\(\dfrac{1}{2}\cdot\left(\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+..+\dfrac{1}{9}-\dfrac{1}{11}\right)\)
=\(\dfrac{1}{2}\cdot\left(1-\dfrac{1}{11}\right)\)
=\(\dfrac{1}{2}\cdot\dfrac{10}{11}\)
=\(\dfrac{5}{11}\)
\(S=\dfrac{1}{3}+\dfrac{1}{15}+\dfrac{1}{35}+...+\dfrac{1}{99}\\ =\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{9.11}\\ =1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{9}-\dfrac{1}{11}\\ =1-\dfrac{1}{11}\\ =\dfrac{10}{11}\)
