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Proving an Increasing Sequence (a question about the answer)
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[QUOTE="CompuChip, post: 4542396, member: 81086"] All a(n) are defined as the square root of their predecessor, and the square root is always non-negative. If you want to be completely rigorous, you can prove it inductively: assume that a(k) ≥ 0 for all k ≤ n. Then in particular a(n) ≥ 0, therefore a(n) + 2 ≥ 2 (> 0), so a(n + 1) is the square root of a non-negative number which is itself non-negative. And the base step -- a(1) ≥ 0 -- is trivial. [/QUOTE]
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Proving an Increasing Sequence (a question about the answer)
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