Đáp án:

 `D = 5/14`

Giải thích các bước giải:

 Ta có:

`D = 10/56 + 10/140 + 10/260 + ....+ 10/1400`

`D = 5/28 + 5/70 + .....+ 5/700`

`D = 5/(4.7) + 5/(7.10) + ......+ 5/(25.28)`

`3.D = 3. (5/(4.7) + 5/(7.10) + ......+ 5/(25.28))`

`3/5. D = 3. (1/(4.7) + 1/(7.10) +.....+ 1/(25. 28))`

`3/5. D = 3/(4.7) + 3/(7.10) + ....+ 3/(25.28)`

( Áp dụng `k/(n. (n+k)) = 1/n - 1/(n+k)` ta có: )

`3/5. D = 1/4 - 1/7 + 1/7 - 1/10+ .....+ 1/25 - 1/28`

`3/5 . D = 1/4 - 1/28`

`3/5.D = 7/28 - 1/28 = 6/28 = 3/14`

`D = 3/14 : 3/5`

`D = 5/14`

Vậy `D = 5/14`

@Active Activity

Đáp án:

$\dfrac{5}{14}$

Giải thích các bước giải:

$\dfrac{10}{56}$ +$\dfrac{10}{140}$ +$\dfrac{10}{260}$ ........+$\dfrac{10}{1400}$ 

$D$ $=$ $\dfrac{5}{28}$ +$\dfrac{5}{70}$ +$\dfrac{5}{130}$ ........+$\dfrac{5}{700}$

$D$ $=$ $\dfrac{5}{4.7}$ +$\dfrac{5}{7.10}$ +$\dfrac{5}{10.13}$ ........+$\dfrac{5}{25.28}$ 

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

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

$D$ $=$ $\dfrac{5}{3}$ $.$ $($ $\dfrac{1}{4}$ -$\dfrac{1}{28}$ $)$

$D$ $=$ $\dfrac{5}{3}$ $.$ $($ $\dfrac{7}{28}$ -$\dfrac{1}{28}$ $)$

$D$ $=$ $\dfrac{5}{3}$ $.$ $\dfrac{3}{14}$ $=$ $\dfrac{5}{14}$ 

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