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Infinitely Continued III (Posted on 2010-02-04) Difficulty: 3 of 5

√(6+2√(7+3√(8+4√(9+5√(10+ ....)))))

See The Solution Submitted by K Sengupta    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Is my reasoning valid? Spoiler | Comment 5 of 7 |
(In reply to re: Is my reasoning valid? Spoiler by Harry)

Nice work, Harry.  

Yes, this does pave the way for a proof by induction that f(x) = x for all positive x. Jer's method works fine, starting with x = 3.  If f(3) = 3, then f(4) = 4 and f(5) = 5 and so on, and so on.

And that makes the problem solution = 4, just as Charlie said.

I am interested to hear about the behavior of f(x) when x is positive and non-integral, but at first blush my intuition says that f(x) = x for all x. 

  Posted by Steve Herman on 2010-02-06 11:10:21
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