Question

Tính nhanh:

\(\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)

Answer 1

\(\frac{10}{56}+\frac{10}{140}+...+\frac{10}{1400}\)

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

\(=\frac{5}{3}\left(\frac{3}{28}+\frac{3}{70}+...+\frac{3}{700}\right)\)

\(=\frac{5}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{25.28}\right)\)

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

\(=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{28}\right)\)

\(=\frac{5}{3}.\frac{3}{14}=\frac{5}{14}\)