Question

A=10/56+10/140+10/260+......+10/1400

Answer 1

A=10/56+10/140+10/260+...+10/1400

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

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

  =\(\frac{5}{3}\)(\(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\))

  =\(\frac{5}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)

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

  =\(\frac{5}{3}.\frac{3}{14}\)

  =\(\frac{5}{14}\)