TA có: \(H=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+\ldots+\frac{10}{1400}\)

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

\(=\frac{5}{4\cdot7}+\frac{5}{7\cdot10}+\frac{5}{10\cdot13}+\cdots+\frac{5}{25\cdot28}\)

\(=\frac53\left(\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+\cdots+\frac{3}{25\cdot28}\right)\)

\(=\frac53\left(\frac14-\frac17+\frac17-\frac{1}{10}+\cdots+\frac{1}{25}-\frac{1}{28}\right)\)

\(=\frac53\left(\frac14-\frac{1}{28}\right)=\frac53\cdot\frac{6}{28}=\frac{30}{84}=\frac{5}{14}\)

Rút gọn rồi tách mẫu là đ

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

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

\(\dfrac{3A}{5}=\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{25}-\dfrac{1}{28}\)

\(\dfrac{3A}{5}=\dfrac{1}{4}-\dfrac{1}{28}=\dfrac{3}{14}\)

⇒ \(A=\dfrac{5}{14}\)

- Ồ hay anh/chị. Em đang nghĩ không ra :)

\(=\frac{20}{112}+\frac{20}{280}+\frac{20}{520}+...+\frac{20}{2800}=20\left(\frac{1}{8.14}+\frac{1}{14.20}+\frac{1}{20.26}+...+\frac{1}{50.56}\right)\)

\(=20\left(\frac{1}{8}-\frac{1}{56}\right)=20.\frac{3}{28}=\frac{15}{7}\)

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

= 5/28 + 5/70 + 5/130 + ... + 5/700

= 5/4.7 + 5/7.10 + 5/10.13 + ... + 5/25.28

= 5.1/3.(3/4.7 + 3/7.10 + 3/10.13 + ... + 3/25.28)
= 5/3.(1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + ... + 1/25 - 1/28)
= 5/3.(1/4 - 1/28)
= 5/3.3/14

= 5/14

M=5/28+5/70+...+5/700

M=5/4.7+5/4.10+...+5/25.28

3/5M=1/4-1/28

3/5M=3/14

M=5/14