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Is It Infinitely Increasing? (Posted on 2004-09-30) Difficulty: 3 of 5
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)

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Some Thoughts 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
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