Solution-Prove that a bounded sequence

Prove that a bounded sequence

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Reference no: EM131396656

a) Let {x_n} be a bounded sequence. Prove that if limn→∞ sup |x_n| = 0, then limn→∞ x_nexists and equals 0.

(b) Prove that a bounded sequence that does not converge always has at least two subsequences that converge to different limits.

(d) Find the set of all subsequential limits for the sequence {x_n} if for all n ∈ N

Reference no: EM131396656

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Prove that a bounded sequence

Reference no: EM131396656

Reference no: EM131396656

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