# Convergence of a Sequence

by Icebreaker
Tags: convergence, sequence
 P: n/a "Let $$k\in \mathbb{N}$$ and $$a_0=k$$. Let $$a_n=\sqrt{k+a_{n-1}}, \forall n\geq1$$ Prove that $$a_n$$ converges." If we look at the similar sequence b_0 = k and b_n = sqrt(a_n-1), then that sequence obviously converges to 1. Unfortunately, b_n
But you don't know if $\lim a_n$ exists.