Problem

Find at least 10 partial sums of the series. Grap…

04:29

Problem 10 Easy Difficulty

Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial sums on the 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.
$ \displaystyle \sum_{n = 1}^{\infty} \cos n $

Answer

divergent

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 2

Series

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Watch More Solved Questions in Chapter 11

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Problem 81

Problem 82

Problem 83

Problem 84

Problem 85

Problem 86

Problem 87

Problem 88

Problem 89

Problem 90

Problem 91

Problem 92

Video Transcript

let's find atleast ten partial sums of the Siri's. So to do that, we'LL just find as one as two always Teo as ten These are the first ten partial zones and so I'll actually do that and graft them at the same time. So we go to my graphing calculator and Dez Mose And then here let me a raise this and graph iss So here are my first ten sums the first cordon and is telling you the value of end. So here here's s one and then the value is point five four and so on and going all the way up to the S ten, which is about negative one point four one seven. So here you can pause this screen and the right coordinates are giving you the first ten values. So now that's a graph of the sequence of partial sums. So we already graft that, and on the graph, we saw the values of the partial sums. So then there's another part Here were to graft the sequence of terms. So here would. They also would like to see a one a two all the way to a ten where Anne is just coastline of n. So let's also graph in a different color. Let me a race the graph for a moment of the partial sums and let me put in the graph of the ends. So here the co sign values Excuse me? Not yet. So there we go and purple. We see the graph of the co signs. I have a label there. If you want deposit, you could record those right hand values. Otherwise, I'll just remove the labels. And if we just look at this purple graph, we can see that it doesn't look like the values will converge. And if you like, I'LL go ahead and you can plot both the sequence and and purple and the partial sums and red. So coming back to the original problem does it appear that the Siri's convergence or diverges by the graph it looks like it diverges. So I'll go back to the graph and read. We can see that it doesn't really look like the values are approaching anything, so that's a guess. But if you want a precise answer, you can show the limit of co sign, and it doesn't exist, so cannot be zero. So the Siri's diverges bye the divergence test, and that's our final answer

Problem