\(\frac{1}{2.4}+\frac{1}{4.6}+....+\frac{1}{2016.2018}\)
\(=\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{2016.2018}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{2018}\right)=\frac{1}{2}.\frac{504}{1009}=\frac{252}{1009}\)
\(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{2016.2018}\)
\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2016}-\frac{1}{2018}\)
\(=\frac{1}{2}+\left(-\frac{1}{4}+\frac{1}{4}\right)+\left(-\frac{1}{6}+\frac{1}{6}\right)+...+\left(-\frac{1}{2016}+\frac{1}{2016}\right)-\frac{1}{2018}\)
\(=\frac{1}{2}+0+0+0+...+0-\frac{1}{2018}\)
\(=\frac{1}{2}-\frac{1}{2018}\)
\(=\frac{1009}{2018}-\frac{1}{2018}\)
\(=\frac{1008}{2018}=\frac{504}{1009}\)
Ai thấy tớ đúng k nha
