Đáp án:

Giải thích các bước giải:

1)

$\displaystyle \begin{array}{{>{\displaystyle}l}} A=\frac{-3+\frac{3}{20} -\frac{3}{13} +\frac{3}{2015}}{7-\frac{7}{20} +\frac{7}{13} -\frac{7}{2015}} -1\\ =\frac{-3\left( 1-\frac{1}{20} +\frac{1}{13} -\frac{1}{2015}\right)}{7\left( 1-\frac{1}{20} +\frac{1}{13} -\frac{1}{2015}\right)} -1\\ =-\frac{3}{7} -1\\ =-\frac{10}{7}\\ B=3+\frac{1}{1.2} +\frac{1}{2.3} +...+\frac{1}{2014.2015}\\ =3+\left( 1-\frac{1}{2}\right) +\left(\frac{1}{2} -\frac{1}{3}\right) +...+\left(\frac{1}{2014} -\frac{1}{2015}\right)\\ =3+1-\frac{1}{2015}\\ =\frac{8059}{2015} \end{array}$

2)

$\displaystyle \begin{array}{{>{\displaystyle}l}} A\leqslant x+1\leqslant B\\ \Leftrightarrow -\frac{10}{7} \leqslant x+1\leqslant \frac{8059}{2015}\\ \Leftrightarrow -\frac{17}{7} \leqslant x\leqslant \frac{6044}{2015} \ ( x\in \mathbb{N})\\ \Leftrightarrow x=\{0;1;2\} \end{array}$