Compute the Limit of a Recursive Sequence

Recursive sequences of the form may be viewed as discrete dynamical systems. The limit (fixed point) of such a dynamical system can be computed directly using RSolveValue, as illustrated in the following.

Compute the limit of a linear recursive sequence.

Visualize the convergence of the sequence to its limiting value.

The nested radical may be regarded as the limit of a nonlinear recursive sequence.

Compute the exact value of the nested radical.

The equation can be solved by computing the limit of the following trigonometric recursive sequence.

Calculate the limit to an arbitrary precision.

Visualize the convergence of the sequence to its limiting value.