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Power to the 2 (Posted on 2004-02-20) Difficulty: 2 of 5
What is the limit to this sequence?

√(2)
√(2+√(2))
√(2+√(2+√(2)))
√(2+√(2+√(2+√(2))))...

In general, what is the sequence in terms of x if 2 is replaced with x?

  Submitted by Gamer    
Rating: 2.8750 (8 votes)
Solution: (Hide)
By seeing that y = √(x + y), you can square each side, then subtract y from both sides and factor to get: y(y-1) = x, the answer to the second problem.

Substituting 2 in for x and solving gives y = 2, or the answer to the first problem.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
answerK Sengupta2007-07-11 05:15:07
seems simple enuffred_sox_fan_0320032004-02-26 21:43:43
re: SolutionNick Hobson2004-02-23 14:02:27
Solutionre: a guesssandy2004-02-22 00:55:00
SolutionSolutionLarry2004-02-21 10:27:53
a guesssandy2004-02-21 04:21:34
Some Thoughtsextraneous solutionsTristan2004-02-20 17:25:04
NiceRoberto Mattos2004-02-20 12:29:14
No Subjectgulrez2004-02-20 11:07:43
SolutionSumFederico Kereki2004-02-20 08:47:53
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