Is It Infinitely Increasing? (Posted on 2004-09-30)

	Submitted by Old Original Oskar!
Rating: 3.0000 (8 votes)
Solution:	(Hide)
3. This was posed by the indian mathematician Ramanujan. Let's prove, using induction, that m+1= S(m)= 1√(1+m√(1+(m+1)√(1+...))). Obviously, for m=0, S(0)=1. We can write m+1=1√(1+mS(m+1)) and squaring gets m²+2m+1=1+mS(m+1) that agrees with S(m+1)=m+2.

	Subject	Author	Date
	Answer	K Sengupta	2008-03-01 10:45:36
	re(2): Solution by Googling	Richard	2004-10-13 17:39:07
	re: Solution by Googling	David Shin	2004-10-13 13:07:04
	Solution by Googling	Richard	2004-10-13 01:03:52
	re(2): interesting	Bon	2004-10-06 03:42:48
	re: interesting	Ira Jewell	2004-10-01 17:41:26
	re(3): interesting	David Shin	2004-10-01 10:35:34
	re(2): interesting	e.g.	2004-10-01 08:06:25
	re: interesting	e.g.	2004-10-01 07:38:43
	interesting	Larry	2004-10-01 04:06:02
	re: hi	RandyOrton	2004-09-30 15:08:53
	re: hi	e.g.	2004-09-30 14:55:10
	hi	ayala	2004-09-30 14:32:34