Câu hỏi 156
Chứng minh đẳng thức
$$
\frac{n!}{x(x+1)(x+2)\dots(x+n)} = \frac{\binom{n}{0}}{x} - \frac{\binom{n}{1}}{x+1} + \frac{\binom{n}{2}}{x+2} - \dots + (-1)^n \frac{\binom{n}{n}}{x+n}.
$$
$$
\frac{n!}{x(x+1)(x+2)\dots(x+n)} = \frac{\binom{n}{0}}{x} - \frac{\binom{n}{1}}{x+1} + \frac{\binom{n}{2}}{x+2} - \dots + (-1)^n \frac{\binom{n}{n}}{x+n}.
$$