Question

[☆MĭηɦღAηɦ❄]

Tính :

M = 5/1.2.3 + 5/2.3.4 + 5/3.4.5 + ... + 5/10.11.12

Ai nhanh mk tk nha !!

Answer 1

[Arima Kousei]

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 !!!

Answer 2

[Arima Kousei]

Công thức : 

\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{6}\right)=\frac{1}{2}.\frac{1}{3}=\frac{1}{1.2.3}\)