Evaluate \(u_n\) for small \(n\), conjecture a formula, then prove it's correct:
$$\begin{align}
& u_1 = 2 \\
& u_{n + 1} = \dfrac{u_n}{1 + u_n} \\
& u_n = \mathord{?}
\end{align}$$

$$\begin{array}{ll}
\lvert z_1 \rvert = r_1 & \arg(z_1) = \theta_1 \\
\lvert z_2 \rvert = r_2 & \arg(z_2) = \theta_2 \\
\lvert z_1z_2 \rvert = r_1r_2 & \arg(z_1 + z_2) = \theta_1 + \theta_2
\end{array}$$