i) Let {an} be a sequence satisfying an> 5 for n >> 1. If {an} converges to L, then L> 5. j) Suppose that the sequence {an /n} converges. Then {an} converges. k) Consider a sequence {an} for which the sequence {} converges. Then {an} converges.

i) Let {an} be a sequence satisfying an> 5 for n >> 1. If {an} converges to L, then L> 5. j) Suppose that the sequence {an /n} converges. Then {an} converges. k) Consider a sequence {an} for which the sequence {} converges. Then {an} converges.

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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D̲e̲t̲e̲r̲m̲i̲n̲e̲ ̲i̲f̲ ̲e̲a̲c̲h̲ ̲o̲f̲ ̲t̲h̲e̲ ̲f̲o̲l̲l̲o̲w̲i̲n̲g̲ ̲s̲t̲a̲t̲e̲m̲e̲n̲t̲s̲ ̲i̲s̲ ̲t̲r̲u̲e̲ ̲o̲r̲ ̲f̲a̲l̲s̲e̲.̲ ̲I̲f̲ ̲f̲a̲l̲s̲e̲,̲ ̲p̲r̲o̲v̲i̲d̲e̲ ̲a̲ ̲p̲r̲e̲c̲i̲s̲e̲ ̲c̲o̲u̲n̲t̲e̲r̲e̲x̲a̲m̲p̲l̲e̲,̲ ̲i̲f̲ ̲t̲r̲u̲e̲ ̲g̲i̲v̲e̲ ̲a̲ ̲v̲e̲r̲y̲ ̲b̲r̲i̲e̲f̲ ̲j̲u̲s̲t̲i̲f̲i̲c̲a̲t̲i̲o̲n̲.̲ ̲T̲h̲a̲n̲k̲ ̲y̲o̲u̲!̲.

(i) Let {an} be a sequence satisfying an> 5 for n » 1.
If {an} converges to L, then L> 5.
(j) Suppose that the sequence {an /n} converges. Then {an} converges.
(k) Consider a sequence {an} for which the sequence {} converges. Then {an} converges.

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