Suppose that xn R. a) Prove that {xn} is bounded if and only if there is

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Suppose that xn ∊ R.
a) Prove that {xn} is bounded if and only if there is a C > 0 such that |xn| < C for all n ∊ N.
b) Suppose that {xn} is bounded. Prove that xn/nk → 0, as n → ∞, for all k ∊ N.
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