How much is 1√(1+ 2√(1+ 3√(1+ 4√(1+ 5√(...)))))? Does it tend to infinity?

Note: the initial 1 is just for completeness!

(In reply to interesting by Larry)

If Larry's numbers are correct, it would suggest that 1√(1+n√(1+(n+1)√(1+(n+2)√(1+(n+3)√(...)))))=n+1; , which could probably be proved by induction on n. (At least the formula is obviously true for n=0.)

Posted by e.g. on 2004-10-01 07:38:43