1. The sequence $\left(a_{n}\right)$ is defined recursively:

$$
\begin{aligned}
& a_{0}=0 \\
& a_{n}=n+a_{n-1}, \quad n \in \mathbf{N}
\end{aligned}
$$

To which number is $a_{2006}$ equal?
Solution.

We have

$$
a_{n}=1+2+\ldots+2006=\frac{2005 \cdot 2006}{2}=2011015
$$