x - arctan(x) is continuous and is 0 at 0, its derivative is 1 - 1/(1+x^2) which is positive when x>0 .... I see no problem here, it is an increasing function.
It seems like this should be a fairly simple thing, yet I can't seem to pin down the trick.
Hi, all. I need to prove that if , then .
Any ideas?
POTENTIALLY USELESS INFO: This is in order to prove that recursively defined by and converges to a finite limit.
Thanks!