tính M = 10/56+10/140+10/416+.....+10/1400
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
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
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
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
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\dfrac{5}{28}+\dfrac{5}{70}+\dfrac{5}{130}+...+\dfrac{5}{700}\)
\(\dfrac{3A}{5}=\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+...+\dfrac{3}{25.28}\)
\(\dfrac{3A}{5}=\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{25}-\dfrac{1}{28}\)
\(\dfrac{3A}{5}=\dfrac{1}{4}-\dfrac{1}{28}=\dfrac{3}{14}\)
⇒ \(A=\dfrac{5}{14}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt S= 5/28 + 5/70 + 5/130 +.....+5/700
= 5/4.7 + 5/7.10 + ......+ 5/ 25.28
3S/5=1/4-1/7+1/7-1/10+.....+1/25-1/28
3S/5=1/4-1/28
3S/5=3/14
3S=3/14x5
3S=15/14
S=15/14x1/3
S=15/42
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)