MathDB

Problem 4

Part of 1995 VJIMC

Problems(1)

limit of arctan^n(x)

Source: VJIMC 1995 2.4

11/25/2021
Let {xn}n=1∞\{x_n\}_{n=1}^\infty be a sequence such that x1=25x_1=25, xn=arctan⁡(xn−1)x_n=\operatorname{arctan}(x_{n-1}). Prove that this sequence has a limit and find it.
limitsreal analysistrigonometry