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(Solution) - Let bk be a real sequence and b R a

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Let {bk} be a real sequence and b ? R.
a) Suppose that there are M, N ? N such that |b - bk| < M for all k > N. Prove that

Let {bk} be a real sequence and b ? R.
</p><p> </p><p>a)
for all n > N.
b) Prove that if bk ? b as k ? ?, then
Let {bk} be a real sequence and b ? R.
</p><p> </p><p>a)
as n ? ?.
c) Show that the converse of b) is false.


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This question was answered on: Jul 11, 2017

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