- #1

student34

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## Homework Statement

__Question from my professor:__"Consider the sequence {a(n)} (from n=1 to ∞) deﬁned inductively by a(1) = 0, and a(n+1) = √(a(n) + 2) for n ≥ 1. Prove that {a(n)} (from n=1 to ∞) is increasing".

__Here's the first part of the answer from my professor:__"Consider a(n+1)^2 − (a(n))^2 = a(n) + 2 − (a(n))^2 = −(a(n)^2 − a(n) −2) = −(a(n) − 2)(a(n) + 1).

**Note that a(n) ≥ 0 for all n**. For a(n) ∈ [−1,2] we see that −(a(n) −2)(a(n) + 1) ≥ 0. The initial element a(1) = 0 belongs to the interval [0,2]".

How does he know that a(n) ≥ 0 for all n? Is this a given of some sort?

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