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


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

See The Solution Submitted by Gamer    
Rating: 2.8750 (8 votes)

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Nice | Comment 3 of 10 |
If we call S the 'n' term of this sequence, like:
S = √(2+√(2+√(2+...
and we square both sides of the equation, we will reach:
S² = 2+S
S=(1(+/-)√(1+2*4))/2, and considering only the positive solution as valid for our purpose, we reach S=2 as being the limit to this sequence.
And if 2 is replaced with X, the solution would be S=((1+√(1+4*X))/2 (again considering only the positive solution as valid for us).
  Posted by Roberto Mattos on 2004-02-20 12:29:14
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