tailieunhanh - Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 60

Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 60. A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course | Infinite Geometric Series 571 PROBLEMS FOR SECTION For Problems 1 through 11 determine whether the series converges or diverges. If it converges find its sum. 1. 1 - 10 - 100------ -10 2. - - - - 3. 2 - 2 - 27 - - 3 - 4. 3 - 2 - 6 - - 2 3 - 5. 1 - 1 - 4- - is ------- 6 1 _ 1 1 _ 1 .4 8 - 16 32 - 7. 2 - 1 - 3 - 9 ---- 4 - 8------------ 12 3 - 9. e - 1 - e-1 - e-2 - e-3 ----- 10. 2e - 2e2 - 2e3 - - 2e - 11. 2e -2 - 2e -3 - 2e -4 - - 2e - - 12. Find the sum of the following. If there is no finite sum say so. a 3 - 9 - 27 - - 320 2 2 2 2 3 2 b 3 - 3 - 3 - - 3 - c 10 - 100 - 1000 - d 3 - 3 - 3 2 - 3 3 - e - - 2 - 3 - f 1 - x2 - x4 - x6 - for -1 x 1 13. Determine whether each of the following geometric series converges or diverges. If the series converges determine to what it converges. a _4 _ 1 _ 3 _ 9 a 3 2 16 128 - b __Li _ b 100 - 100 2 100 3 - 100 4 c 7 77 7__ c 10000 - 11000 12100 - 13310 d 1 - x - x2 - x3 - for x 1 14. Write each of the following series first as a repeating decimal and then as a fraction. a 2 2 -I--2--1---2--L- . . . a 2 - 10 - 100 - 1000 - b 3 -102-104-106- 572 CHAPTER 18 Geometric Sums Geometric Series A MORE GENERAL DISCUSSION OF INFINITE SERIES In the previous four sections we focused on geometric sums and geometric series. In this section we broaden our discussion to investigate other inflnite series. Our focus in this chapter is geometric series but you will have a better appreciation of geometric series if you have some familiarity with series that are not geometric. Given an inflnite series a1 an the most basic question to consider is whether the series converges or diverges. Suppose all the terms of the inflnite series are positive. Then Sn S n the sum of the flrst n terms is an increasing function. We know from our study of functions that an increasing function may increase without bound or it may