Problem

Determine whether the geometric series is converg…

02:04

Problem 21 Easy Difficulty

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.
$ \displaystyle \sum_{n = 1}^{\infty} 12(0.73)^{n-1} $

Name: determine whether the geometric series is convergent or divergent if it is convergent find its sum d
Uploaded: 2018-02-19
Duration: 2 min 32 s
Channel: Numerade
Description: Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. $ \displaystyle \sum_{n = 1}^{\infty} 12(0.73)^{n-1} $

Answer

$$\frac{400}{9}$$

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

Grace H.

Catherine R.

Missouri State University

Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham

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 determine whether this geometric series is conversion or divergent, and if it's conversion, will go and find the summer as well. So recall geometric Siri's of this form, then hear this converges. If the absolute Value bar is strictly less than one sonar problem, we see our his point seven three, and the absolute value of that is just point seven three. That's less than one. So this converges that answers the first question. So come up here we'LL see. It's convergence, not divergent. And now, for convergent geometric series, we have a formula for the sun and equals one twelve, and we have our our point seven three to the end minus one. So, of course, here, when I wrote the Geometric series, it doesn't matter whether you have n here and minus one. It's still geometric. So in this case, the formula is we always take the first term of the entire series that will correspond to plugging in the starting number down here, the first number and equals one into an over here, and I don't give you the first time and then one minus R. So if we go ahead and plug in and equals one. We have twelve point seven three to the one minus one. That's point seven three to the zero. Power is just one, so we could ignore that term and then one minus point seven three. So I'm getting twelve over point two seven. This can be simplified, too. See twelve over twenty seven over one hundred. And that simplifies too. Four hundred over nine. And that's our final answer. This's the sum of the geometric Siri's.

J H.

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 2

Series

Problem