Question: 4. Let (In) be a sequence in R and suppose that (Xn) coverges to a E R. Assume that Xn 2 0 for all n

4. Let (In) be a sequence in R and suppose that (Xn) coverges to a E R. Assume that Xn 2 0 for all n E N. Show that a 2 0 and that the sequence (VIn) converges to va. (Hint: you may use that In - a = (VXn - Va) (Van + va) for all n E N and treat the case a = 0 separately.)

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