Let {a,}, {bn} and {cn} be sequences of real numbers. Which of the following statements are true? I. If {an} is convergent and {b,} is bounded, then {a,bn} is convergent. II. If lim an = L and lim bn = o, then lim a,b, = oo. III. If an +0 for all n e Zt and lim no an 0, then lim a, = oo. IV. If lim an = 0 and {b,} is bounded, then n00 lim a,bn = 0. V. If b, < an < en for all n e Zt, {bn} and {cn} are convergent, then {an} is also convergent. VI. If {an} is unbounded, then {an} is divergent. I, II I, IV (a) (b) (c) IV, VI (d) I, III, V (e) III, IV, V

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.