Help with contractive sequence proof

1. Oct 24, 2004

Ed Quanta

Can someone help me prove that the following sequence is contractive?

Let a1= 1 and an+1=1/5(an)^2 - 1

I understand the definition of a contractive sequence, but I am not sure how to formally prove this,

2. Oct 24, 2004

HallsofIvy

Staff Emeritus
Okay, what is the definition of a "contractive sequence"? I know the definition of a "contractive mapping" but I don't recall seeing it applied to a sequence!