My teacher gave us a definition to what he calls a contractive sequence which basically means that:
being $u(n)$ a sequence of real numbers: $u(n)$ is a contractive sequence if there's a constant $C∈ ]0,1[$ such that $$ |u_{n+1}-u_n|\le C|u_n-u_{n-1}| $$ for a large enough n value.
I've tried to understand this as sequence whose two consecutive terms decrease at a certain rate (C). However, I cannot fully understand this. If someone could help me visualize this or understand it better I would appreciate it.
Thank you for your time.