+ \(\frac{1}{n\left(n+1\right)\left(n+2\right)}=\frac{1}{2}\cdot\frac{2}{n\left(n+1\right)\left(n+2\right)}\) \(=\frac{1}{2}\cdot\frac{\left(n+2\right)-n}{n\left(n+1\right)\left(n+2\right)}=\frac{1}{2}\left[\frac{1}{n\left(n+1\right)}-\frac{1}{\left(n+1\right)\left(n+2\right)}\right]\)
Do đó : \(E=30\left(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{98\cdot99\cdot100}\right)\)
\(E=30\cdot\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+...+\frac{1}{98\cdot99}-\frac{1}{99\cdot100}\right)\)
\(E=15\cdot\left(\frac{1}{2}-\frac{1}{9900}\right)=15\cdot\frac{4949}{9900}=\frac{4949}{660}\)
