Domain of the function

[Loki123]

What is the domain? I thought it's - infinity, +infinity, but it's not. Why?

 

[Dr.Peterson]

What is the domain? I thought it's - infinity, +infinity, but it's not. Why?
View attachment 32347

It isn't a polynomial; it's a power series. For example, what do you get for x=2? for x=1/2?

What do you know about convergence?

 

[JeffM]

[math]f(x) = \sum_{j=0}^{\infty} (-x)^j[/math]
Is f(x) a real number if [imath]|x| \ge 1[/imath]?

 

[Loki123]

It isn't a polynomial; it's a power series. For example, what do you get for x=2? for x=1/2?

What do you know about convergence?

nothing i think. what do i need to know?

 

[Loki123]

[math]f(x) = \sum_{j=0}^{\infty} (-x)^j[/math]
Is f(x) a real number if [imath]|x| \ge 1[/imath]?

i am not sure. probably not, i don't know what it would up to later.

 

[BigBeachBanana]

i am not sure. probably not, i don't know what it would up to later.

Don't you see it's an infinite geometric series with a=1, r=-x?
Jeff is hinting you at the condition for the series to converge.

 

[Loki123]

Don't you see it's an infinite geometric series with a=1, r=-x?
Jeff is hinting you at the condition for the series to converge.

i saw that, but i am not sure how jeff's hint is supposed to help me...

 

[BigBeachBanana]

i saw that, but i am not sure how jeff's hint is supposed to help me...

What's the condition for the series to converge?

 

[Loki123]

What's the condition for the series to converge?

according to my research, r>1 so x<1

 

[BigBeachBanana]

according to my research, r>1 so x<1

Not quite. A geometric series converges when [imath]|r|<1[/imath]. Try again

 

[Loki123]

Not quite. A geometric series converges when [imath]|r|<1[/imath]. Try again

so x<1

 

[Loki123]

so x<1

and -x<1, x>-1

 

[BigBeachBanana]

and -x<1, x>-1

You might have the right answer in your head, but you wrote it wrong. Try again.

 

[Loki123]

You might have the right answer in your head, but you wrote it wrong. Try again.

∣-x∣<1
1. case -x, -x>0 that is x<0
2. case x, -x<0 that is x>0

1. condition
-x<1 that is x>-1
2. condition
x<1
final (-1,1)

 

[Dr.Peterson]

What do you know about convergence?

nothing i think. what do i need to know?

This is one of those cases where it would be really helpful if you would tell us what you have learned, so we can more quickly determine how to most effectively help you, rather than trying lots of things and being told you don't know them yet.

I take it that you aren't learning about power series, or about convergence of series at all, which in a calculus class is where I would expect this problem to be assigned. You seem even to have forgotten about geometric series, a more basic context in which they might ask this question.

Maybe you've said something about what you are studying in other threads, but can you tell us the context for this one?

 

[Loki123]

This is one of those cases where it would be really helpful if you would tell us what you have learned, so we can more quickly determine how to most effectively help you, rather than trying lots of things and being told you don't know them yet.

I take it that you aren't learning about power series, or about convergence of series at all, which in a calculus class is where I would expect this problem to be assigned. You seem even to have forgotten about geometric series, a more basic context in which they might ask this question.

Maybe you've said something about what you are studying in other threads, but can you tell us the context for this one?

it's complicated. my class is doing combinations, variations and permutations right now. However, i have these problems to practice for a test that does not necessarily care for our school program so I have problems that do not involve what I have learned. In that case I try to learn how to solve the problem as simply as i can (which is not good, ik)

 

[Steven G]

and -x<1, x>-1

For the record, -x<1 is exactly the same as x>-1.
The answer is |x|<1 which breaks down to ...?

 

[Steven G]

∣-x∣<1
1. case -x, -x>0 that is x<0
2. case x, -x<0 that is x>0

1. condition
-x<1 that is x>-1
2. condition
x<1
final (-1,1)

What you wrote is correct but you should just realize that |-x| = |x|.

 

[Loki123]

What you wrote is correct but you should just realize that |-x| = |x|.

How do I know if a series converges or diverges (and what does that even mean)?

 

[Dr.Peterson]

How do I know if a series converges or diverges (and what does that even mean)?

I will repeat: In order to help you, we need to know what you have learned about this topic.

If you have never heard of convergence, then this problem is not for you.

If you need to learn everything on this test even though it is not in your curriculum, then why have you not searched for lessons on convergence, geometric series, and other terms that have been mentioned, so you can learn it? We can't teach you everything from scratch; we are here to help you with what you are learning elsewhere.