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Let (xn) be a sequence with positive terms. (a) Prove the following: lim inf xn+1/ xn...

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Advance Math

Let (xn) be a sequence with positive terms. (a) Provethe following: lim inf xn+1/ xn ≤ lim infn√ xn ≤ lim sup n√xn ≤lim sup xn+1/ xn .

(b) Give example of (xn) where all above inequalitiesare strict. Hint; you may consider the following sequencexn = 2n if n even and xn = 1 if nodd.

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