\(C=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2017}-\frac{1}{2018}\)
\(C=1-\frac{1}{2018}\)
\(C=\frac{2017}{2018}\)
\(C=\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+.....+\frac{1}{2017x2018}\)
Ta thấy \(\frac{1}{1x2}=\frac{1}{1}-\frac{1}{2}\)
\(\frac{1}{2x3}=\frac{1}{2}-\frac{1}{3}\)
.............................................
\(\frac{1}{2017x2018}=\frac{1}{2017}-\frac{1}{2018}\)
\(\Rightarrow C=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{2017}-\frac{1}{2018}\)
\(\Rightarrow C=\frac{1}{1}-\frac{1}{2018}\)
\(\Rightarrow C=\frac{2017}{2018}\)
Chúc bạn học tốt nhớ k mình nhá
\(C=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2017.2018}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2017}-\frac{1}{2018}=1-\frac{1}{2018}=\frac{2017}{2018}\)