\(D=\dfrac{10}{56}+\dfrac{10}{140}+\dfrac{10}{260}+...+\dfrac{10}{1400}\)
\(=\dfrac{5}{28}+\dfrac{5}{70}+\dfrac{5}{130}+....+\dfrac{5}{700}\)
\(=5\left(\dfrac{1}{28}+\dfrac{1}{70}+\dfrac{1}{130}+...+\dfrac{1}{700}\right)\)
\(=5\left(\dfrac{1}{4.7}+\dfrac{1}{7.10}+\dfrac{1}{10.13}+...+\dfrac{1}{25.28}\right)\)
\(=5.\dfrac{1}{3}\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+...+\dfrac{1}{25}-\dfrac{1}{28}\right)\)
\(=\dfrac{5}{3}\left(\dfrac{1}{4}-\dfrac{1}{28}\right)\)
\(=\dfrac{5}{3}.\dfrac{3}{14}\)
\(=\dfrac{5}{14}\)
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