MathNet 2023-part-01 — 191 problems (EN–VI) Question 136

Let $x_0, x_1, \dots$ be a sequence of real numbers such that $x_0 = 1$ and $x_{n+1} = \sin(x_n) + \frac{\pi}{2} - 1$ for all $n \ge 0$. Show that the sequence converges and find its limit.

(Kristyan Vasilev)