Find the limit of the following sequence or determine that the sequence diverges. \[ \left\{\left(1+\frac{20}{n}\right)^{n}\right\} \]

To find the limit of the sequence defined by \[ a_n = \left(1+\frac{20}{n}\right)^{n}, \] we can recognize that this expression is reminiscent of the limit definition of the exponential function. Specifically, we recall the well-known limit: \[ \lim_{n \to \infty} \left(1 + \frac{x}{n}\right)^{n} = e^{x}. \] In our case, we have \( x = 20 \). Thus, we can apply this result: \[ \lim_{n \to \infty} a_n = \lim_{n \to \infty} \left(1+\frac{20}{n}\right)^{n} = e^{20}. \] Therefore, the limit of the sequence is \[ \boxed{e^{20}}. \]