S=\(\dfrac{2}{4}+\dfrac{2}{12}+\dfrac{2}{24}+...+\dfrac{2}{4900}\)
S=\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{2450}\)
S=\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}\)
S=\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\)
S=\(1-\dfrac{1}{50}=\dfrac{49}{50}\)
Vậy S=\(\dfrac{49}{50}\)
\(S=\dfrac{2}{4}+\dfrac{2}{12}+\dfrac{2}{24}+...+\dfrac{2}{4900}\)
\(S=\dfrac{2}{2.2}+\dfrac{2}{2.6}+\dfrac{2}{4.6}+...+\dfrac{2}{50.98}\)
\(\Rightarrow\dfrac{1}{2}S=\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...+\dfrac{2}{98.100}\)
\(\dfrac{1}{2}S=\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{98}-\dfrac{1}{100}\)
\(\dfrac{1}{2}S=\dfrac{1}{2}-\dfrac{1}{100}\)
\(\dfrac{1}{2}S=\dfrac{49}{100}\)
\(\Rightarrow S=\dfrac{49}{100}:\dfrac{1}{2}\)
\(\Rightarrow S=\dfrac{49}{50}\)
