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

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

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

3S/5=3/4.7+3/7.10+3/10.13+...+3/25.28

3S/5=1/4-1/7+1/7-1/10+1/10-1/13+....+1/25-1/28

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

3S/5=3/14

S=3/14.5/3

S=5/14

Vậy S=5/14

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

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

3S/5=3/4.7+3/7.10+3/13.10+.........+3/25.28

3S/5=1/4-1/7+1/7-1/10+1/10-1/13+.........+1/25-1/28

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

3S/5=3/14

S=3/14.5/3

S=5/14

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

S=5/4x7+5/7x10+5/10x13+.....+5/25x28

Sx3/5=3/4x7+3/7x10+.......+3/25x28

Sx3/5=1/4-1/7+1/7-1/10+1/10+.....+1/25-1/28

Sx3/5=1/4+(1/7-1/7)+(1/9-1/9)+.....+(!/25-1/25)-1/28

Sx3/5=1/4-1/28

Sx3/5=3/14

S=3/14 : 3/5

S=5/14

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

\(\frac{5}{14}\)   Là đúng đó bn 

nhớ k cho mình nha! hjhj

\(A=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)

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

\(\frac{3A}{5}=\frac{3}{4\times7}+\frac{3}{7\times10}+\frac{3}{10\times13}+...+\frac{3}{25\times28}\)

\(\frac{3A}{5}=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\)

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

\(\frac{3A}{5}=\frac{3}{14}\)

\(A=\frac{3}{14}\times\frac{5}{3}\)

\(A=\frac{5}{14}\)

@py. Hello, hihi

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 

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)

=(7-4)/(4.7)+(10-7)/(7.10)+(13-10)/(10.13)+...+(28-25)/(25.28)

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

Rồi ta chuyển tử số thành 1

=1/4-1/7+1/7-1/10+1/10-1/13+...+1/25-1/28

=1/4-1/28

=3/14

\(A=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+..+\frac{10}{1400}\)

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

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

\(A.\frac{3}{5}=\frac{7-4}{4.7}+\frac{10-7}{7.10}+\frac{10-13}{10.13}+..+\frac{28-15}{25.28}\)

\(A.\frac{3}{5}=\frac{7}{4.7}-\frac{4}{4.7}+\frac{10}{7.10}-\frac{7}{7.10}+\frac{13}{13.10}+...+\frac{25}{25.28}-\frac{28}{25.28}\)

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

\(A.\frac{3}{5}=\frac{1}{4}-\frac{1}{28}=\frac{6}{28}=\frac{3}{14}\)

\(A=\frac{3}{14}:\frac{3}{5}=\frac{5}{14}\)

A= 

56

10

 

 + 

140

10

 

 + 

260

10

 

 +..+ 

1400

10

 

 

 

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=

5

28

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70

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5

700

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28

5

 

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70

5

 

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130

5

 

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700

5

 

 

 

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3

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3

7.10

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10.13

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.

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+

3

25.28

A. 

5

3

 

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4.7

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7.10

3

 

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10.13

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25.28

3

 

 

 

 

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.

+

28

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15

25.28

A. 

5

3

 

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25.28

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3

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.

.

.

+

25

25.28

−

28

25.28

A. 

5

3

 

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4

 

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10

 

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1

25

−

1

 

28

A. 

5

3

 

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1

 

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7

1

 

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7

1

 

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10

1

 

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10

1

 

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1

 

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28

1

 

 

 

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3

5

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4

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28

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28

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4

1

 

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28

1

 

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28

6

 

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14

3

 

 

 

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=

3

14

:

3

5

=

5

14

A= 

14

3

 

 : 

5

3

 

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14

5

 

 

 

 

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

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

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

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

⇒ \(A=\dfrac{5}{14}\)