2.7. Solve the equation

$$
1-\frac{x}{1}+\frac{x(x-1)}{2!}-\ldots+(-1)^{n} \frac{x(x-1) \ldots(x-n+1)}{n!}=0
$$
2.7. Answer: $x=1,2, \ldots, n$. The equality

$$
1-\frac{k}{1}+\frac{k(k-1)}{2!}-\ldots+(-1)^{k} \frac{k(k-1) \cdot \ldots \cdot 2 \cdot 1}{k!}=(1-1)^{k}=0
$$

shows that the numbers $k=1,2, \ldots, n$ are roots of this equation. The equation cannot have more than $n$ roots, since its degree is $n$.