Stitz-Zeager_College_Algebra_e-book

One full revolution accounts for 2 84 of the radian

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Unformatted text preview: esson worth remembering. We close this section with a peek into Calculus by considering infinite sums, called series. Consider the number 0.9. We can write this number as 0.9 = 0.9999... = 0.9 + 0.09 + 0.009 + 0.0009 + . . . From Example 9.2.1, we know we can write the sum of the first n of these terms as n 0. 9 · · · 9 = .9 + 0.09 + 0.009 + . . . 0. 0 · · · 0 9 = n − 1 zeros n nines k=1 9 10k Using Equation 9.2, we have n k=1 9 9 = k 10 10 1− 1 10n+1 = 1 − 1 1 10n+1 1− 10 1 It stands to reason that 0.9 is the same value of 1 − 10n+1 as n → ∞. Our knowledge of exponential 1 1 expressions from Section 6.1 tells us that 10n+1 → 0 as n → ∞, so 1 − 10n+1 → 1. We have 7 Any non-terminating just argued that 0.9 = 1, which may cause some distress for some readers. decimal can be thought of as an infinite sum whose denominators are the powers of 10, so the phenomenon of adding up infinitely many terms and arriving at a finite number is not as foreign of a concept as it may appear. We end...
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