 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Is It Infinitely Increasing? (Posted on 2004-09-30) 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!

 See The Solution Submitted by Old Original Oskar! Rating: 3.0000 (8 votes) Comments: ( Back to comment list | You must be logged in to post comments.) interesting | Comment 4 of 13 | As e.g. points out, it seems to be equal to 3.

In addition, starting farther along in the sequence yields interesting results.  For example:
2��(1+ 3��(1+ 4��(1+ 5��(...))))  -------->  8
3��(1+ 4��(1+ 5��(1+ 6��(...))))  -------->  15
.
.
.
n��(1+ (n+1)��(1+ (n+2)��(1+ (n+3)��(...))))  -------->  n^2 - 1

and also

��(1+ 3��(1+ 4��(1+ 5��(...))))  -------->  4
��(1+ 4��(1+ 5��(1+ 6��(...))))  -------->  5
��(1+ 5��(1+ 6��(1+ 7��(...))))  -------->  6
etc...

 Posted by Larry on 2004-10-01 04:06:02 Please log in:

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