Question

Cho H = 10/56 + 10/140 + 10/260 +........+ 10/1400.

Tính H .

Answer 1

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

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

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

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

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

\(\Rightarrow\frac{3H}{5}=\frac{3}{14}\)

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

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

Vậy \(H=\frac{5}{14}\)