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The Nuts and Bolts of Proofs, 4th Edition
book

The Nuts and Bolts of Proofs, 4th Edition

by Antonella Cupillari
January 2011
Beginner content levelBeginner
296 pages
11h 43m
English
Academic Press
Content preview from The Nuts and Bolts of Proofs, 4th Edition
Since n is a positive number, we will just use n >
1
4ε
1
2
q
: Thus, we can use N
ε
=
1
4ε
1
2
q
: Note that this
square root is well defined only when ε 1/2. When ε > 1/2, the condition ja
n
1
2
j< ε is always satisfied
because the largest value of ja
n
1
2
j is achieved by a
1
= 1/3. So the largest value of ja
n
1
2
j is 1/6.
Finding a limit is not always simple. There are several clues that can help. Here is a simple one regarding
the sign of the limit.
EXAMPLE 4.5.7
The limit of a positive sequence cannot be negative. The limit of a negative sequence cannot be positive.
(Note that the limit could be zero.)
Proof: Intuitively this conclusion seems to make sense,
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Publisher Resources

ISBN: 9780123822178