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1. Mark each statement True or False. Justify each answer. (a) If (sm) is a sequence and s; = Sj, then i= j. (b) If sn→ s, then for every ɛ> 0 there exists Ne N such that n>N implies |Sn-s|< E. (c) If s→ k and t,> k, then S,= t, for all n e N. (d) Every convergent sequence is bounded. %3D

1. Mark each statement True or False. Justify each answer. (a) If (sm) is a sequence and s; = Sj, then i= j. (b) If sn→ s, then for every ɛ> 0 there exists Ne N such that n>N implies |Sn-s|< E. (c) If s→ k and t,> k, then S,= t, for all n e N. (d) Every convergent sequence is bounded. %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Mark each statement True or False. Justify each answer. (a) If (sn) is a sequence and s; = Sj, (b) If s, →s, then for every ɛ> 0 there exists Ne N such that n>N implies |Sn-s|< ɛ. (c) If sn→ k and t„ → k, then S,= t, for all n e N. (d) Every convergent sequence is bounded. then i = j. 2. Mark each statement True or False. Justify each answer. (a) If sn→0, then for every ɛ> 0 there exists Ne N such that n>N implies Sn < E. (b) If for every ɛ > 0 there exists Ne N such that n>N implies s, < E, then Sn→ 0. (c) Given sequences (s,) and (a,), if for some s e R, k > 0 and m e N we have |Sn-s| < kļa, for all n> m, then lim s, =s. (d) If sns and sn→t, then s t. = S. %3D
Transcribed Image Text:1. Mark each statement True or False. Justify each answer. (a) If (sn) is a sequence and s; = Sj, (b) If s, →s, then for every ɛ> 0 there exists Ne N such that n>N implies |Sn-s|< ɛ. (c) If sn→ k and t„ → k, then S,= t, for all n e N. (d) Every convergent sequence is bounded. then i = j. 2. Mark each statement True or False. Justify each answer. (a) If sn→0, then for every ɛ> 0 there exists Ne N such that n>N implies Sn < E. (b) If for every ɛ > 0 there exists Ne N such that n>N implies s, < E, then Sn→ 0. (c) Given sequences (s,) and (a,), if for some s e R, k > 0 and m e N we have |Sn-s| < kļa, for all n> m, then lim s, =s. (d) If sns and sn→t, then s t. = S. %3D
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