Question

[Conan]

Tính tổng : \(R=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)

 Ai nhanh nhất mình sẽ tick cho ^_^ nhớ kb với mình nhé

Answer 1

[l҉o҉n҉g҉ d҉z҉]

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

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

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

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

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

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

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