Đặt :
\(M=\dfrac{1}{4}+\dfrac{1}{28}+\dfrac{1}{70}+................+\dfrac{1}{550}\)
\(\Rightarrow M=\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+..................+\dfrac{1}{22.25}\)
\(\Rightarrow3M=\dfrac{3}{1.4}+\dfrac{3}{4.7}+.................+\dfrac{3}{22.25}\)
\(\Rightarrow3M=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+.........+\dfrac{1}{22}-\dfrac{1}{25}\)
\(\Rightarrow3M=1-\dfrac{1}{25}\)
\(\Rightarrow3M=\dfrac{24}{25}\)
\(\Rightarrow M=\dfrac{24}{75}\)
Đặt:
\(A=\dfrac{1}{4}+\dfrac{1}{28}+\dfrac{1}{70}+.....+\dfrac{1}{550}\)
\(A=\dfrac{1}{1.4}+\dfrac{1}{4.7}+\dfrac{1}{7.10}+.....+\dfrac{1}{22.25}\)
\(A=\dfrac{1}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+.....+\dfrac{1}{22}-\dfrac{1}{25}\right)\)
\(A=\dfrac{1}{3}\left(1-\dfrac{1}{25}\right)=\dfrac{1}{3}.\dfrac{24}{25}=\dfrac{25}{72}\)
