3-ча 1. Find the roots of the equation

\[
1-\frac{x}{1}+\frac{x(x-1)}{2!}-\cdots+(-1)^{n} \frac{x(x-1) \ldots(x-n+1)}{n!}=0
\]
Solve 1. Answer: \(1,2, \ldots, n\). The equality

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

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