Question

[Ichijo]

Tính S =1/14+1/35+1/65+...+1/350

Answer 1

[Yen Nhi]

`Answer:`

\(S=\frac{1}{14}+\frac{1}{35}+\frac{1}{65}+...+\frac{1}{350}\)

\(\Rightarrow S=\frac{2}{28}+\frac{2}{70}+\frac{2}{130}+...+\frac{2}{700}\)

\(\Rightarrow S=\frac{2}{4.7}+\frac{2}{7.10}+\frac{2}{10.13}+...+\frac{2}{25.28}\)

\(\Rightarrow S=\frac{2}{3}\left(\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{25.28}\right)\)

\(\Rightarrow S=\frac{2}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)

\(\Rightarrow S=\frac{2}{3}.\frac{3}{14}\)

\(\Rightarrow S=\frac{1}{7}\)