a) Để phân số $\frac{2n+14}{n+2}$ là phân số tối giản
$\rightarrow$ $2n+14$ $\vdots$ $n+2$
$\rightarrow$ $2n+4+12$ $\vdots$ $n+2$
$\rightarrow$ $2(n+2)+ 12 $ $\vdots$ $n+2$
Mà $2(n+2)$ $\vdots$ $n+2$
$\rightarrow$ $12$ $\vdots$ $n+2$
$\rightarrow$ $n+2$ $\in$ $Ư(12)$ $=$ {$\pm1, \pm2, \pm3, \pm4, \pm6, \pm12$}
Mà $n \in N$
$\rightarrow$ $n+2 \geq 2$
$\rightarrow$ $n+2$ $\in$ $Ư(12)$ $=$ {$2, 3, 4, 6, 12$}
$\rightarrow$ $n \in$ {$0, 1, 2, 4, 10$}
b) $A = (\frac{1}{2} -1)(\frac{1}{3} -1)(\frac{1}{4} -1) ... (\frac{1}{200} -1)$
$A = (\frac{-1}{2})(\frac{-2}{3})(\frac{-3}{4}) ... (\frac{-199}{200})$
$A = (-1)^{199} \times (\frac{1}{2})(\frac{2}{3})(\frac{3}{4}) ... (\frac{199}{200})$
$A = (-1) \times (\frac{1 \times 2 \times 3\times ... \times 199}{2 \times 3 \times 4 \times ... \times 200})$
$A = (-1) \times \frac{1}{200} = \frac{-1}{200}$
Mà $\frac{-1}{200} < \frac{-1}{199} $
$\rightarrow A < \frac{-1}{199} $
