Unformatted text preview: we do not connect the dots in a pleasing
fashion as we are used to doing, because the domain is just the whole numbers in this case, not a
collection of intervals of real numbers. If you feel a sense of nostalgia, you should see Section 1.2.
y
3
2 1
1
2 −1
2 1 2 3 x −1
−3
2 Graphing y = bk = (−1)k
,k≥0
2k + 1 Speaking of {bk }∞ , the astute and mathematically minded reader will correctly note that this
k=0
technically isn’t a sequence, since according to Deﬁnition 9.1, sequences are functions whose domains
are the natural numbers, not the whole numbers, as is the case with {bk }∞ . In other words, to
k=0
satisfy Deﬁnition 9.1, we need to shift the variable k so it starts at k = 1 instead of k = 0. To
see how we can do this, it helps to think of the problem graphically. What we want is to shift
the graph of y = b(k ) to the right one unit, and thinking back to Section 1.8, we can accomplish
this by replacing k with k − 1 in the deﬁnition of {bk }∞ . Speciﬁcally, let ck = b...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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