Question

Tính tổng S = 10/56 + 10/140 + 10/260 +.......+ 10/1400

Giúp mk với 

Answer 1

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

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

\(\frac{3S}{5}=\frac{3}{4}\times7+\frac{3}{7}\times10+\frac{30}{10}\times13+........+\frac{3}{25}\times28\)

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

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

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

\(S=\frac{3}{14}\times\frac{5}{3}\)

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

Vậy \(S=\frac{5}{14}\)