M=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

=5/3(3/4.7+3/7.10+3/10.13+...+3/25.28)

=5/3(1/4-1/7+1/7-1/10+1/10-1/1+...+1/25-1/28)

=5/3.(1/4-1/28)

=5/3.3/14

=5/14

khó @gmail.com

Sửa đề: \(M=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+\cdots+\frac{10}{1400}\)

Ta có: \(M=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+\cdots+\frac{10}{1400}\)

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

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

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

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

\(=\frac53\left(\frac14-\frac{1}{28}\right)=\frac53\cdot\frac{6}{28}=\frac53\cdot\frac{3}{14}=\frac{5}{14}\)

M=5/28+5/70+...+5/700=5/4.7+5/7.10+...+5/25.28=>3M=5(1/4-1/7+1/7-1/10+...+1/25-1/28)

=>3M=5(1/4-1/28)=>3M=15/14=>M=5/14

Đầu tiên rút gọn M trước 
M= 5/28 + 5/70 +.....+10/700 
= 5/(4.7)+5/(7.10)+....5/(25.28) 
3M= 5( 1/4 - 1/7 +1/7-1/10+......+1/25-1/28) 
3M= 5 (1/4-1/28) 
3M=15/14 
M= 5/14 :D 

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

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

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

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

⇒ \(A=\dfrac{5}{14}\)

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

@py. Hello, hihi

bài này bạn chỉ cần tách mẫu ra là làm được thôi