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Stitz-Zeager_College_Algebra_e-book

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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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