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need help on a math equation...?
its called infinite surds which i have never heard of before...but thats beside the point. ok im trying to determine a formula for a_(n+1) in terms of a_(n) and the sequence is sqrt1 + sqrt1 +sqrt1 + .... and so on. if anyone knows how to help me go about determining an equation for such a series it would be greatly appreciated
1 Answer
- jeredwmLv 61 decade agoFavorite Answer
I assume that this formula is non-trivial, and thus I assume that what you mean is
√(1+√(1+√(1+√(1+...)))), rather than
√1 + √1 + √1 + ....
The formula here is pretty simple;
a_(n+1) = √(1+a_n).
To find the limit (if it exists), simply note that if there is a limit A, then it will be positive and satisfy the equation
A = √(1+A).
To prove that a limit must exist, note simply that this is an increasing sequence, and show that it is bounded above by 2.
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