HH_Sec_9_2

# HH_Sec_9_2 - Math 10B Lecture Examples Section 9.2...

This preview shows pages 1–2. Sign up to view the full content.

(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 0 1 2 A B s 0 1 2 A B s 0 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 of Calculus by Hughes-Hallett et al.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern