=1/1.3+1/3.5+...+1/2017.2019
=1/2.(2/1.3+2/3.5+...+2/2017.2019)
=1/2.[(1-1/3)+(1/3-1/5)+...+(1/2017-1/2019)]
=1/2.(1-1/2019)
=1/2.2018/2019
=2017/403
=1009/2019
tk cho mk nhe
\(=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{2017.2019}\right)\)\(=\frac{1}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2017}-\frac{1}{2019}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1}-\frac{1}{2019}\right)\)\(=\frac{1}{2}.\frac{2018}{2019}\)\(=\frac{1009}{2019}\)
Bài làm :
Ta có :
\(\frac{1}{1.3}+\frac{1}{3.5}+....+\frac{1}{2017.2019}\)
\(=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+....+\frac{2}{2017.2019}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{2017}-\frac{1}{2019}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1}-\frac{1}{2019}\right)\)
\(=\frac{1}{2}.\frac{2018}{2019}\)
\(=\frac{1009}{2019}\)
Chúc bạn học tốt !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
