If (an) is a decreasing sequence of strictly positive numbers and if an is convergent, show that lim(nan) = 0.
If (an) is a decreasing sequence of strictly positive numbers and if ∑an is convergent, show that lim(nan) = 0.
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Related Book For 
Introduction to Real Analysis
4th edition
Authors: Robert G. Bartle, Donald R. Sherbert
ISBN: 978-0471433316