We're interested in solving to get a value for , using Newton's iteration .

I must show that for any , holds.

I've tried algebraically to show the inequality but I failed in every attempts.

For instance if I can show that then I'd be done.

Or equivalently if .

I have a strong feeling that I should use a well known inequality to show this straightforwardly, but I don't know which one.

I'd like some help. Thanks in advance.