(a)If Sn is a convergent sequence, then |Sn| is also a convergent sequence and (b) State the converse of the statement of the first part. Is the converse true? If so, prove it. If not, give a counterexample. If you don't have time to solve all problems, just show me question (b).

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 1YT
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Using the definition of convergence to show: 
(a)If Sn is a convergent sequence, then |Sn| is also a convergent sequence and
(b) State the converse of the statement of the first part. Is the converse true? If so, prove
it. If not, give a counterexample.
If you don't have time to solve all problems, just show me question (b).
lim |sn| = | lim sn.
Sn
n→∞
n→∞
Transcribed Image Text:lim |sn| = | lim sn. Sn n→∞ n→∞
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