\(S=\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{2018.2020}\)
\(S=\frac{1}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{2018.2020}\right)\)
\(S=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2018}-\frac{1}{2020}\right)\)
\(S=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{2020}\right)\)
Tự tính
S=1/2.4+1/4.6+1/6.8+...+1/2018.2020
S=1/2.(2/2.4+2/4.6+2/6.8+...+2/2018.2020)
S=1/2.(1-1/4+1/4-1/6+1/6-1/8+...+1/2018-1/2020)
S=1/2.(1-1/2020)
S=1/2.(2020/2020-1/2020)
S=1/2.2019/2020
S=2019/4040
\(S=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2018}-\frac{1}{2020}\right)\)
\(S=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{2020}\right)\)
\(S=\frac{1}{4}-\frac{1}{4040}=\frac{1010}{4040}-\frac{1}{4040}=\frac{1009}{4040}\)
2S = \(\frac{1}{2}\)- \(\frac{1}{4}\)+\(\frac{1}{4}\)- \(\frac{1}{6}\)+ \(\frac{1}{6}\)- \(\frac{1}{8}\)+ ... +\(\frac{1}{2018}\)- \(\frac{1}{2020}\)
2S = \(\frac{1}{2}\)- \(\frac{1}{2020}\)
2S = \(\frac{1009}{2020}\)
S = \(\frac{1009}{2020}\): 2
S = \(\frac{1009}{4040}\)
\(4S=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{1009\cdot1010}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{1009}-\frac{1}{1010}\)
\(=1-\frac{1}{1010}\)
\(=\frac{1009}{1010}\)
\(S=\frac{1009}{4040}\)
\(\text{Giải :}\)
\(S=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2018}-\frac{1}{2020}\right)\)
\(S=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{2020}\right)\)
\(S=\frac{1}{4}-\frac{1}{4040}=\frac{1010}{4040}-\frac{1}{4040}=\frac{1009}{4040}\)
\(\text{~~Học tốt~~}\)
Trả lời:
\(S=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{2018.2020}\)
\(=\frac{1.2}{2.4.2}+\frac{1.2}{4.6.2}+\frac{1.2}{6.8.2}+...+\frac{1.2}{2018.2020.2}\)
\(=\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2018.2020}\right)\)
\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2018}-\frac{1}{2020}\right)\)
\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{2020}\right)=\frac{1}{2}.\frac{1009}{2020}=\frac{1009}{4040}\)
\(\text{Trả lời : }\)
\(S=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2018}-\frac{1}{2020}\right)\)
\(S=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{2020}\right)\)
\(S=\frac{1}{4}-\frac{1}{4040}=\frac{1010}{4040}-\frac{1}{4040}=\frac{1009}{4040}\)
\(\text{Vậy S = }\frac{1009}{4040}\)
