Mathematics 4{5 - Phillips Exeter Academy

Mathematics 4 5 Mathematics DepartmentPhillips Exeter AcademyExeter, NHJuly 2017To the StudentContents: Members of the PEA Mathematics Department have written the material in thisbook. As you work through it, you will discover that algebra, geometry, and trigonometryhave been integrated into a mathematical whole. There is no Chapter 5, nor is there a sectionon tangents to circles. The curriculum is problem-centered, rather than and theorems will become apparent as you work through the problems, andyou will need to keep appropriate notes for your records there are no boxes containingimportant theorems. There is no index as such, but the reference section that starts on page201 should help you recall the meanings of key words that are defined in the problems (wherethey usually appear italicized).Problem solving: Approach each problem as an exploration. Reading each question care-fully is essential, especially since definitions, highlighted in italics, are routinely insertedinto the problem texts.

Mathematics 4-5 1. Consider the sequence de ned recursively by x n = pp 1996x n 1 and x 0 = 1. Calculate the rst few terms of this sequence, and decide whether it approaches a limiting value.

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