Ta có :
\(M=\frac{5}{1.2.3}+\frac{5}{2.3.4}+...+\frac{5}{10.11.12}\)
\(M=5.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{10.11.12}\right)\)
\(M=5.\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{10.11}-\frac{1}{11.12}\right)\)
\(M=\frac{5}{2}.\left(\frac{1}{1.2}-\frac{1}{11.12}\right)\)
\(M=\frac{5}{2}.\left(\frac{1}{2}-\frac{1}{132}\right)\)
\(M=\frac{5}{2}.\left(\frac{66}{132}-\frac{1}{132}\right)\)
\(M=\frac{5}{2}.\frac{65}{132}\)
\(M=\frac{325}{264}\)
Tham khảo nha !!! Chúc học tốt !!!
Công thức :
\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{6}\right)=\frac{1}{2}.\frac{1}{3}=\frac{1}{1.2.3}\)
