Ch 12. Infinite Sequences and Series ma Multimedia Engineering Math Sequencesand Series Integral andComparison Alt. Series &Abs. Conv. PowerSeries Taylor, Mac. &Binomial
 Chapter 1. Limits 2. Derivatives I 3. Derivatives II 4. Mean Value 5. Curve Sketching 6. Integrals 7. Inverse Functions 8. Integration Tech. 9. Integrate App. 10. Parametric Eqs. 11. Polar Coord. 12. Series Appendix Basic Math Units Search eBooks Dynamics Statics Mechanics Fluids Thermodynamics Math Author(s): Hengzhong Wen Chean Chin Ngo Meirong Huang Kurt Gramoll ©Kurt Gramoll

MATHEMATICS - CASE STUDY

Introduction

Problem Diagram
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An import and export company has rented a warehouse for storage. The warehouse is fully stocked with goods when the company was first established in January. The net stockpile for each month in the first six months is summarized in the table on the left. Based on this trend, the manager of the company would like to know whether the size of this warehouse is suitable for long term storage.

Questions

Table: Monthly Stockpile for the
First Six Months

 Month Net Stockpile January 1 February -1/2 March +1/3 April -1/4 May +1/5 June -1/6

Based on the data summarized in the table, can it be represented using a series? What type of series? If so, find the sum of the series for a period of 12 months. What is the error involved in this approximation?

Approach

• Find the partial sum of the series for n = 12 and use this to approximate for the occupancy of the warehouse in long run.
• If the warehouse is at least half-occupied, then it is considered suitable.