Đáp án:

`↓`

Giải thích các bước giải:

`a/b = 1/3 + 1/4 + 1/5 + ... + 1/10`

`a/b = ( 1/10 + 1/3 ) + ( 1/9 + 1/4 ) + ( 1/8 + 1/5 ) + ( 1/7 + 1/6 )`

`a/b = 13/30 + 13/36 + 13/40 + 13/42`

`=>` Ta có MSC là: `30 * 36 * 40 * 42`

Gọi các thừa số phụ là: `x_1; x_2; x_3; x_4`

`=> a/b = ( 13 * x_1 )/( 30 * 36 * 40 * 42 ) + ( 13 * x_2 )/( 30 * 36 * 40 * 42 ) + ( 13 * x_3 )/( 20 * 36 * 40 * 42 ) + ( 13 * x_4 )/( 30 * 36 * 40 * 42 )`

`=> a/b = ( 13 * x_1 + 13 * x_2 + 13 * x_3 + 13 * x_4 )/( 30 * 36 * 40 * 42 )`

`=> a/b = ( 13 * ( x_1 + x_2 + x_3 + x_4 ) )/( 30 * 36 * 40 * 42 )`

`=> a = 13 * ( x_1 + x_2 + x_3 + x_4 )`

`=> a \vdots 13`

`=> ĐPCM`

`#Sad`

Đáp án + Giải thích các bước giải:

Bài 5: Tổng $\frac{1}{3}$ $\text{+}$ $\frac{1}{4}$ $\text{+}$ $\frac{1}{5}$ $\text{+ ... +}$ $\frac{1}{10}$ bằng phân số $\frac{a}{b}$. Chứng tỏ rằng $\text{a}$ chia hết cho $\text{13}$.

$\frac{1}{3}$ $\text{+}$ $\frac{1}{4}$ $\text{+}$ $\frac{1}{5}$ $\text{+ ... +}$ $\frac{1}{10}$ $\text{=}$ $\frac{a}{b}$

$\Rightarrow$ $\frac{a}{b}$ $\text{=}$ $\text{(}$$\frac{1}{3}$ $\text{+}$ $\frac{1}{10}$$\text{)}$ $\text{+}$ $\text{(}$$\frac{1}{4}$ $\text{+}$ $\frac{1}{9}$$\text{)}$ $\text{+}$ $\text{(}$$\frac{1}{5}$ $\text{+}$ $\frac{1}{8}$$\text{)}$ $\text{+}$ $\text{(}$$\frac{1}{6}$ $\text{+}$ $\frac{1}{7}$$\text{)}$

$\Rightarrow$ $\frac{a}{b}$ $\text{=}$ $\frac{13}{30}$ $\text{+}$ $\frac{13}{36}$ $\text{+}$ $\frac{13}{40}$ $\text{+}$ $\frac{13}{42}$

$\Rightarrow$ $\frac{a}{b}$ $\text{=}$ $\text{13}$ $\times$ $\text{(}$$\frac{1}{30}$ $\text{+}$ $\frac{1}{36}$ $\text{+}$ $\frac{1}{40}$ $\text{+}$ $\frac{1}{42}$$\text{)}$

$\Rightarrow$ $\text{a}$ $\text{=}$ $\text{13}$ $\times$ $\text{(}$$\frac{1}{30}$ $\text{+}$ $\frac{1}{36}$ $\text{+}$ $\frac{1}{40}$ $\text{+}$ $\frac{1}{42}$$\text{)}$$\text{.}$ $\text{b}$ $\vdots$ $\text{13}$

$\Rightarrow$ $\text{a}$ $\vdots$ $\text{13}$