Can you check to see if this is even a valid question. I got this challenge from someone and I believe there's no way to solve it but have a look. I can't find a perfect bounded above value...I tried one, no good, tried 2, 3, 4, won't work.
Thanks in advance
This is a calculus type problem.
Given
a1= 3 as in 'a subscript 1'
For n greater than or equal to an+1 = sqrt of 3+an
SHOW an is increasing and bounded above. SHOW an (a subscript n) approaches L and find L
FIND Limit an as n approached infinity
If the attached formula is what you mean, not only that the formula has a bound, it is monotonically decreasing, with a limit at: 2.30277563773199, and highest value at n=1 (a1 = 3).
This can be achieved by assuming there is a finite limit, when approaching the limit, An will be equal to An+1, and therefore:
Code:
An = sqrt(An + 3) ==>
An^2 -An - 3 = 0 ==>
An = (1 +- sqrt(13)) / 2
The minus is not an option because the formula is always positive, so:
Code:
An = (1 + sqrt(13)) / 2 = 2.30277563773199...
But I think that this is not the formula you mean...
How can it be decreasing when the question stated show that its increasing, I sort of understand your way of calculating it but I don't think the formula is right.
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