\(\left(\dfrac{1}{1\cdot2\cdot3}+\dfrac{1}{2\cdot3\cdot4}+\dfrac{1}{3\cdot4\cdot5}+...+\dfrac{1}{98\cdot99\cdot100}\right)y=\dfrac{49}{200}\)
\(\dfrac{1}{2}\left(\dfrac{1}{1\cdot2}-\dfrac{1}{2\cdot3}+\dfrac{1}{2\cdot3}-\dfrac{1}{3\cdot4}+\dfrac{1}{3\cdot4}-\dfrac{1}{4\cdot5}+...+\dfrac{1}{98\cdot99}-\dfrac{1}{99\cdot100}\right)y=\dfrac{49}{200}\)
\(\dfrac{1}{2}\left(\dfrac{1}{1\cdot2}-\dfrac{1}{99\cdot100}\right)y=\dfrac{49}{200}\)
\(\left(\dfrac{1}{4}-\dfrac{1}{19800}\right)y=\dfrac{49}{200}\)
\(\left(\dfrac{4950}{19800}-\dfrac{1}{19800}\right)y=\dfrac{49}{200}\)
\(\dfrac{4949}{19800}y=\dfrac{49}{200}\)
\(y=\dfrac{49}{200}:\dfrac{4949}{19800}\)
\(y=\dfrac{99}{101}\)
Vậy \(y=\dfrac{99}{101}\).
\(\left(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{98.99.100}\right)y=\dfrac{49}{200}\\ \Rightarrow\dfrac{1}{2}\left(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+...+\dfrac{1}{98.99}-\dfrac{1}{99.100}\right)y=\dfrac{49}{200}\\ \Rightarrow\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{9900}\right)y=\dfrac{49}{200}\\ \Rightarrow\dfrac{4949}{9900}y=\dfrac{49}{100}\\ \Rightarrow y=\dfrac{99}{101}\)
