HH_Sec_9_2 - (9/1/08) Math 10B. Lecture Examples. Section...

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Unformatted text preview: (9/1/08) Math 10B. Lecture Examples. Section 9.2. Geometric series † Example 1 Suppose you want to go from a point A toward a second point B two miles away. First you go one mile (Figure 1). Then you go a half mile further for a total of 1 + 1 2 miles (Figure 2). Next you go half that distance (Figure 3), and so forth, so that at each stage you go half as far as you did in the previous stage. (a) How far have you gone after one, two, three, five, and eight stages? (b) Predict the limit of your distance from A as the number of stages tends to ∞ . s 1 2 A B s 1 2 A B s 1 2 A B FIGURE 1 FIGURE 2 FIGURE 3 Answer: (a) See the table below. (b) The distance seems to be approaching 1 1- 1 2 = 2 miles. Stages Distance (miles) Decimal approximation 1 1 1 1–2 1 + 1 2 1 . 5 1–3 1 + 1 2 + ( 1 2 ) 2 1 . 75 1–5 1 + 1 2 + ( 1 2 ) 2 + ( 1 2 ) 3 + ( 1 2 ) 4 1 . 9375 1–8 1 + 1 2 + ( 1 2 ) 2 + ( 1 2 ) 3 + ( 1 2 ) 4 + ( 1 2 ) 5 +( 1 2 ) 6 + ( 1 2 ) 7 1 . 9921875 † Lecture notes to accompany Section 9.2 ofLecture notes to accompany Section 9....
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This note was uploaded on 09/13/2010 for the course MATH math 10b taught by Professor Reed during the Summer '10 term at UCSD.

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HH_Sec_9_2 - (9/1/08) Math 10B. Lecture Examples. Section...

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