It is proved by definition that if xn > 0 (n = 1,2,...), and lim (n →∝) xn = a > = 0, then LIM (n →∝) √ xn = √ a
lim(n→ ∝) xn=a
For any √ a * ε > 0, there exists n > 0 such that for any n > n there is | xn-a | 0
For ε 0
So there is
|Xn-a | = | (√ xn) ^ 2 - (√ a) ^ 2 | = | [xn - √ a | * | [xn + √ a | 0, there exists n > 0 such that for any n > n there is | [xn - √ a]|
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