10. Let {an}, {bn} and {en} be sequences of real numbers Which of the following statements are true? I. If {an} is convergent and {bn} is bounded, then {anbn} is convergent. II. If lim an = L and lim bn = ∞, then n-x n-x lim anbn = ∞. n→∞ III. If an #0 for all n € Z and lim n→∞ an lim an = ∞. 84x IV. If lim an = n4x = 0, then 0 and {bn} is bounded, then lim anbn = 0. nx V. If bn ≤ an ≤ en for all n € Z+, {bn} and {cn) are convergent, then {an} is also convergent. VI. If {a} is unbounded, then {an} is divergent. (a) I, II (b) I, IV (c) IV, VI (d) I, III, V (e) III, IV, V

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