7. (10 points) Observe: $1 \times 2 \times 3 \times 4+1=5^{2}$.
$$
\begin{array}{l}
2 \times 3 \times 4 \times 5+1=11^{2}, \\
3 \times 4 \times 5 \times 6+1=19^{2},
\end{array}
$$
(1) Please write a general conclusion and provide a proof;
(2) According to (1), calculate $2000 \times 2001 \times 2002 \times 2003+1$ (express the result in the simplest form).
For the natural number $n$, we have
$$
\begin{array}{l}
n(n+1)(n+2)(n+3)+1 \\
=\left(n^{2}+3 n\right)\left(n^{2}+3 n+2\right)+1 \\
=\left(n^{2}+3 n\right)^{2}+2\left(n^{2}+3 n\right)+1=\left(n^{2}+3 n+1\right)^{2} .
\end{array}
$$
(2) From (1), we get
$$
2000 \times 2001 \times 2002 \times 2003+1=4006001^{2} .
$$