   Chapter 11.2, Problem 10E

Chapter
Section
Textbook Problem

Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial same screen. Does it appear that the series is convergent or divergent? If it is convergent, find the sum. If it is divergent, explain why. ∑ n = 1 ∞ cos n

To determine

To find:

At least 10 partial sums of the series and graph both the sequence of terms and the sequence of partial sums on the same screen then conclude if the convergent or divergent of the series and find sum.

Explanation

1) Concept:

Use a calculator to find at least 10 partial sums, the sequence of terms, and graph. Then use the definition to decide whether the series is divergent.

2) Definition:

A series n=1an is divergent, if the sequence {sn} is divergent.

3) Given:

n=1cos n

4) Calculation:

The table shows 10 partial sums  sn  of the series and the sequence of terms  an:

 n an sn 1 0.54030 0.54030 2 -0.41615 0.12416 3 -0.98999 -0.86584 4 -0.65364 -1.51948 5 0.283662 -1.23582 6 0.96017 -0.27565 7 0.753902 0.47825 8 -0.1455 0.33275 9 -0.91113 -0.57838 10 -0.83907 -1.41745

Graph:

From the graph, the table and using the concept, it appears that, the series n=1cos n diverges, since its terms do not approach to 0.

Use following steps for TI-86 Calculator:

To graph {an} and  {sn}, set the calculator to Param mode under mode button and DrawDot mode

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