Question

Tính giá trị biểu thức:

\(E=\frac{30}{1.2.3}+\frac{30}{2.3.4}+\frac{30}{3.4.5}+...+\frac{30}{98.99.100}\)

Answer 1

\(E=\frac{30}{1.2.3}+\frac{30}{2.3.4}+\frac{30}{3.4.5}+...+\frac{30}{98.99.100}\)

\(E=15\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{98.99.100}\right)\)

\(E=15\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{98.99}-\frac{1}{99.100}\right)\)

\(E=15\left(\frac{1}{1.2}-\frac{1}{99.100}\right)\)

\(E=15.\frac{4949}{9900}\)

\(E=\frac{4949}{660}\)