\(A=\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{2018.2020}\right)\)
\(A=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2018}-\frac{1}{2020}\right)\)
\(A=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{2020}\right)\)
\(A=\frac{1}{2}.\frac{1009}{2020}\)
\(A=\frac{1009}{4040}\)
A=1/2.4+1/4.6+1/6.8+...+1/2018.2020
=1/2(1/2-1/4+1/4-1/6+...+1/2018-1/2020)
=1/2(1/2-1/2020)
=1/2.1009/2020
=1009/4040
#)Giải :
\(A=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{2018.2020}\)
\(\Rightarrow2A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2018.2020}\)
\(2A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2018}-\frac{1}{2020}\)
\(2A=\frac{1}{2}-\left(\frac{1}{4}-\frac{1}{4}\right)-\left(\frac{1}{6}-\frac{1}{6}\right)-\left(\frac{1}{8}-\frac{1}{8}\right)-...-\left(\frac{1}{2018}-\frac{1}{2018}\right)-\frac{1}{2020}\)
\(2A=\frac{1}{2}-0-0-0-...-0-\frac{1}{2020}\)
\(2A=\frac{1}{2}-\frac{1}{2020}\)
\(2A=\frac{1009}{2020}\)
\(\Rightarrow A=\frac{1009}{4040}\)
#)Chúc bn học tốt :D
