Mình làm bừa nha đúng đúng sai sai bạn đừng giận nhé !
\(\frac{1}{2019.2018}-\frac{1}{2018.2017}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
\(=\frac{1}{2019}-\frac{1}{2018}...-\frac{1}{3}-\frac{1}{2}-\frac{1}{2}-\frac{1}{1}\)
\(=\frac{1}{2019}-\left(\frac{1}{2018}-\frac{1}{2018}\right)-..-\frac{1}{1}\)
\(=\frac{1}{2019}-0-\frac{1}{1}=\frac{1}{2019}-\frac{1}{1}\)
\(=-\frac{2018}{2019}\)
\(\frac{1}{2019.2018}-\frac{1}{2018.2017}-...-\frac{1}{3.2}-\frac{1}{2.1}.\)
\(=-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2017.2018}+\frac{1}{2018.2019}\right)\)
\(=-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2017}-\frac{1}{2018}+\frac{1}{2018}-\frac{1}{2019}\right)\)
\(=-\left(1-\frac{1}{2019}\right)=-\frac{2018}{2019}\)
