\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2018}-\frac{1}{2020}\)
\(=\frac{1}{2}-\frac{1}{2020}=\frac{1009}{2020}\)
\(A=\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{2018.2020}\)
\(\Leftrightarrow A=\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{2018.2020}\right)\)
\(\Leftrightarrow A=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{2018}-\frac{1}{2020}\right)\)
\(\Leftrightarrow A=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{2020}\right)=\frac{1}{2}.\frac{1009}{2020}\)
\(\Leftrightarrow A=\frac{1009}{4040}\)
Vậy : \(A=\frac{1009}{4040}\)
Đặt A =\(\frac{1}{2.4}+\frac{1}{4.6}+.....+\frac{1}{2018.2010}\)
\(\Rightarrow2A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+.....+\frac{2}{2018.2020}\)
\(\Rightarrow A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+.....+\frac{1}{2018}-\frac{1}{2020}\)
\(\Rightarrow A=\frac{1}{2}-\frac{1}{2020}\)
\(\Rightarrow A=\frac{1010}{2020}-\frac{1}{2020}\)
\(\Rightarrow A=\frac{1009}{2020}\)
Đặt A =\(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+.....+\frac{1}{2018.2020}\)
⇒2A=\(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+.....+\frac{2}{2018.2020}\)
⇒2A=\(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+.....+\frac{1}{2028}-\frac{1}{2020}\)
⇒2A=\(\frac{1}{2}-\frac{1}{2020}\)
\(\Rightarrow2A=\frac{1010}{2020}-\frac{1}{2020}\)
⇒A=\(\frac{1009}{2020}\div2\)
\(\Rightarrow A=\frac{1009}{4040}\)