Suppose that an is a convergent series of real numbers. Either prove that bn converges

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Suppose that ∑ an is a convergent series of real numbers. Either prove that ∑ bn converges or give a counter-example, when we define bn by
(a) an/n.
(b) √an/n (an > 0),
(c) an sin n.
(d) √an/n (an > 0),
(e) n1/nan,
(f) an/(1 + |an|).
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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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