\(C=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{998\cdot999\cdot1000}\)
\(C=\frac{1}{2}\left[\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+...+\frac{2}{998\cdot999\cdot1000}\right]\)
\(C=\frac{1}{2}\left[\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+...+\frac{1}{998\cdot999}-\frac{1}{999\cdot1000}\right]\)
\(C=\frac{1}{2}\left[\frac{1}{2}-\frac{1}{999\cdot1000}\right]\)
Tính nốt :v
Ta có
\(C=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{998\cdot999\cdot1000}\)
\(\Rightarrow2C=\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+...+\frac{2}{998\cdot999\cdot1000}\)
\(=\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{998\cdot999}-\frac{1}{999\cdot1000}\)
\(=\frac{1}{1\cdot2}-\frac{1}{999\cdot1000}\)
\(=\frac{1}{2}-\frac{1}{999000}\)
\(=\frac{499500}{999000}-\frac{1}{999000}\)
\(=\frac{499499}{999000}\)
\(\Rightarrow C=\frac{499499}{1998000}\)
đúng nha bạn nhớ k mik
