Question

Giải giúp m bài này.

1/1.2.3 + 1/2.3.4 + 1/3.4.5 +......+ 1/998.999.1000

Answer 1

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+....+\frac{1}{998.999.1000}\)

\(=\frac{1}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{998.999.1000}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{998.999}-\frac{1}{999.1000}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{999.1000}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{999000}\right)\)

\(=\frac{1}{2}.\left(\frac{499500}{999000}-\frac{1}{999000}\right)\)

\(=\frac{1}{2}.\frac{499499}{999000}\)

\(=\frac{499499}{1998000}\)

Answer 2

4994999/1998000