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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