Ta có:
\(\frac{2}{3.7}+\frac{2}{7.11}+\frac{2}{11.15}+.....+\frac{2}{2015.2019}\)
\(=2.\left(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+....+\frac{1}{2015.2019}\right)\)
\(=\frac{2}{4}.\left(\frac{2}{3.7}+\frac{2}{7.11}+\frac{2}{11.15}+....+\frac{2}{2015.2019}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+.....+\frac{1}{2015}-\frac{1}{2019}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{2019}\right)\)
\(=\frac{1}{2}.\frac{224}{673}=\frac{112}{673}\)
**** ^^
Đúng 0
Bình luận (0)
