Question

Tính nhanh:

A=\(\dfrac{10}{56}+\dfrac{10}{140}+\dfrac{10}{260}+...........+\dfrac{10}{1400}\)

Answer 1

\(A=\dfrac{10}{56}+\dfrac{10}{140}+\dfrac{10}{260}+...+\dfrac{10}{140}\)

\(=\dfrac{5}{28}+\dfrac{5}{70}+\dfrac{5}{130}+...+\dfrac{5}{700}\)

\(=\dfrac{5}{4.7}+\dfrac{5}{7.10}+\dfrac{5}{10.13}+...+\dfrac{5}{25.28}\)

\(3A=5\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-...-\dfrac{1}{25}+\dfrac{1}{25}-\dfrac{1}{28}\right)\)

\(=5\left(\dfrac{1}{4}-\dfrac{1}{28}\right)\)

\(=5.\dfrac{3}{14}=\dfrac{15}{14}\)

\(\Rightarrow A=\dfrac{15}{14}:3=\dfrac{15}{14}.\dfrac{1}{3}=\dfrac{5}{14}.\)

Vậy \(A=\dfrac{5}{14}.\)