Stitz-Zeager_College_Algebra_e-book

# An angle is said to be in standard position if its

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Unformatted text preview: need a denominator of 10n . Hence, n is 1 2 This is indeed a geometric sequence with ﬁrst term a = 1 and common ratio r = −1. It is an arithmetic sequence with ﬁrst term a = 1 and common diﬀerence d = 1. 9.2 Summation Notation 565 the upper limit of summation. Since n is used in the limits of the summation, we need to choose a diﬀerent letter for the index of summation.3 We choose k and get n 0.9 + 0.09 + 0.009 + . . . 0. 0 · · · 0 9 = n − 1 zeros k=1 9 10k The following theorem presents some general properties of summation notation. While we shall not have much need of these properties in Algebra, they do play a great role in Calculus. Moreover, there is much to be learned by thinking about why the properties hold. We invite the reader to prove these results. To get started, remember, “When in doubt, write it out!” Theorem 9.1. Properties of Summation Notation: Suppose {an } and {bn } are sequences so that the following sums are deﬁned. p • p p (an ± bn ) = n=m p • an...
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