- #1
Icebreaker
"Let [tex]k\in \mathbb{N}[/tex] and [tex]a_0=k[/tex]. Let [tex]a_n=\sqrt{k+a_{n-1}}, \forall n\geq1[/tex] Prove that [tex]a_n[/tex] 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<a_n so I can't use the squeeze theorem.
Any hints would be nice.
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<a_n so I can't use the squeeze theorem.
Any hints would be nice.