\(\dfrac{2}{28}+\dfrac{2}{70}+\dfrac{2}{130}+....+\dfrac{2}{700}\)
\(=\dfrac{2}{4\times7}+\dfrac{2}{7\times10}+\dfrac{2}{10\times13}+...+\dfrac{2}{25\times28}\)
\(=\dfrac{2}{3}\times\left(\dfrac{3}{4\times7}+\dfrac{3}{7\times10}+...+\dfrac{3}{25\times28}\right)\)
\(=\dfrac{2}{3}\times\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-...+\dfrac{1}{25}-\dfrac{1}{28}\right)\)
\(=\dfrac{2}{3}\times\left(\dfrac{1}{4}-\dfrac{1}{28}\right)\)
\(=\dfrac{2}{3}\times\dfrac{6}{28}\)
\(=\dfrac{2}{14}\)
\(=\dfrac{1}{7}\)
Đúng 1
Bình luận (0)
