Question

[Thành Tò Văn]

tính

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

Answer 1

[Thu Thủy]

@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

Answer 2

[Nguyễn Thanh Hằng]

Ta có :

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

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

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

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

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

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

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