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

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\(\frac{5}{14}\)   Là đúng đó bn 

nhớ k cho mình nha! hjhj

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@Thành Tò Văn

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

Ta có :

\(M=\dfrac{10}{56}+\dfrac{10}{140}+\dfrac{10}{260}+...................+\dfrac{10}{1400}\)

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

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

\(\dfrac{3}{5}M=\left(\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+............+\dfrac{1}{25}-\dfrac{1}{27}\right)\)

\(\dfrac{3}{5}M=\dfrac{1}{4}-\dfrac{1}{27}\)

\(\dfrac{3}{5}M=\dfrac{3}{14}\)

\(M=\dfrac{3}{14}:\dfrac{3}{5}=\dfrac{5}{24}\)

\(\dfrac{10}{56}+\dfrac{10}{140}+\dfrac{10}{260}+...+\dfrac{10}{1400}=\dfrac{5}{28}+\dfrac{5}{70}+\dfrac{5}{130}+...+\dfrac{5}{700}\)

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

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

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

\(=\dfrac{5}{3}.\left(\dfrac{1}{4}-\dfrac{1}{28}\right)=\dfrac{5}{3}.\dfrac{3}{14}=\dfrac{5}{14}\)

Chúc bạn học tốt!!!