/sci/ - Science & Math

shameless bump

geometric series, centered at 9, radius of convergence is 1... region of convergence is the open region |x-9|<1

sage for homework thread

Use squeeze theory, find when a^n converges and then find the situation where (x-9) is always less than a

If my post answers your question, delete your thread.. if not, im still here

i just dont understand HOW you figure that out
my book doesnt have any examples and only puts the answers of different types

seriously anyhelp would be much appreciated dude

>>1449541
You may apply the ratio test to show my result. I knew my answer because the geometric series <span class="math">a_n=r^n[/spoiler] converges to <span class="math">\frac{1}{1-r}[/spoiler] if <span class="math">|r|<1[/spoiler]

calc 2 i presume? i hated this bullshit... the worst section of the entire class (and the most useless, arguably)

>>1449541
algebra II book?
what the fuck are you, 15?

>>1449541

Geometric series and P-series, OP. Learn them both. Use them.

>>1449560
lol derp, i'm tired. x < 10 = radius of convergence

>>1449555
by the way, my series was from n=0 to inf, yours appears to be from n=1 to inf.. so yours converges to <span class="math">\frac{1}{1-r}-1[/spoiler] if <span class="math">|r|<1[/spoiler] where <span class="math">r=x-9[/spoiler]

>>1449555

yeah but you can't use that proof because it must follow that 0<r<1... and r will not be less than 1 in all cases due to the variable x.

take the limit of the series... but i onno i completely zonked out for this section and don't remember it

>>1449569

i mean use the ratio test... which involves finding the limit

>>1449565
>>1449560
>lol derp, i'm tired. x < 10 = radius of convergence

No, you forgot the absolute value bars while doing the ratio test. That answer is nonsense.

>>1449557
Did you fail calc II? Infinite series are an extremely powerful and useful tool.

>>1449563

and this isn't a "ro" (P) series you faggot

problem is it askes for 2 xvalues

"Find the valueS of X where the series converges"
so i dont know which 2 to use

>>1449578

i barely got a C lol... gimme a break, the class was at 7:30 in the morning

anything i didn't pick up in the class that i need later in life i'll just re-learn as i need it, like i always do

>>1449569
>yeah but you can't use that proof because it must follow that 0<r<1... and r will not be less than 1 in all cases due to the variable x.

>yeah but you can't use that proof
Yes you can.

> it must follow that 0<r<1
Actually, just |r|<1 is necessary for geometric series of r

> r will not be less than 1 in all cases due to the variable x
Hence a region of convergence. If r=x-9 and |r|<1, then the series converges for |x-9|<1. For real x, this translates to 8<x<10.

>>1449578

and yeah, they're powerful if you're a business degree holder or an economist

not if you're a fucking engineer... we have software called fortran and other shit that to find answers that require numerical methods

>>1449584
| x - 9 | < 1 = radius of convergence.

x = 9 and 8.

>>1449610
derp

8 =< x =< 10

what does it mean when it says "find the sum of the series of values of X"

>>1449583

>implying i implied it was P-series

>>1449602
I'm an electrical engineer and I've seen geometric series as extremely useful in signal processing theory.

>>1449617
>>1449621

but for the sum would i just add the too?

>>1449626

yeah but you probably used some sort of software to hash it out instead of doing it by pen and paper, no?

>>1449617
x must actually be strictly less than 10 and strictly greater than 8, else it diverges to positive and negative infinity respectively.

isn't this a power series?

>>1449637
Well, a computer will do the thousands of calculations necessary for an on-the-spot fourier transform or z-transform but the theory is what I'm talking about. You might be surprised by how often the geometric series crops up in these applications.

>>1449626
>engineer

what does your sexual orientation have do to with anything? im sick of you fuckers always proclaiming "gay pride". Keep that shit to yourself!

>>1449664
A power series is an infinite series.

>>1449653
>x must actually be strictly less than 10 and strictly greater than 8, else it diverges to positive and negative infinity respectively.

It diverges to infinity for x=10
It oscillates (and therefore diverges) for x=8... the partial sums at x=8 oscillate between 0 and 1 and do NOT diverge to an infinity

>>1449665

yes, but still, in today's world, it's pointless for engineers to have to hash this out on paper when it can easily be done with a computer.

>>1449672
lol, I'm straight. I'm an engineer on the outside, but a mathematician at heart.

>>1449674
a power series is a type of infinite series dickwad

>>1449617
herp

8<x<10

It makes a BIG difference.

>>1449676
Blgh.

Haven't done this level of mathematics in one too many terms it appears. :|

I NEED MY FUCKING RATIO TEST BITCHES

On a related note, does anyone else have the bad habit of adding an 'n' to the end of "ratio" occasionally? :|

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>>1449681
>pointless for engineers to have to hash this out on paper when it can easily be done with a computer.
If you're talking about the actual tedious calculations, then of course I agree. But if you're talking about what I think you're talking about (ie, the derivation and understanding of theory) I'd expect an engineer to at least have some clue as to where to math behind this came from. If not, I wouldn't have him or her working on a project involving signal processing.

tl;dr An electrical engineer working in this field should definitely understand this material without relying on some CAS to work the theory out for him.

answer was 8<x<10

but whats the sum?
i cant figure that out now

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>>1449717
<span class="math">\frac{1}{1-r}-1[/spoiler] where r=x-9, I've posted this above.

<span class="math">\frac{1}{10-x}-1[/spoiler]

>>1449737
>>1449737
>>1449737
>>1449737
>>1449737
fucking love you dude
why cant the teached just explain like that hah

>>1449714

i completely agree that engineers need to understand the way the math works, even though they're going to use a program.

but still, in some cases, isn't it better to concentrate on more important theories, like the laws of thermodynamics or the mathematics behind how a steel i-beam will react under certain loads?

i see infinite series as a very specialized tool, that not every engineer in every discipline should have to completely, totally understand.

we use fortran for our diff eq problems, after all...

>>1449743
I don't know. I'm a tutor at my university for this stuff. I know where students struggle, I guess. Also, I'm high as fuck right now :]

>>1449743
Because your teacher doesn't want to give you the answers like the post you're replying to just did...?

:|

>>1449750
>i see infinite series as a very specialized tool, that not every engineer in every discipline should have to completely, totally understand.

I don't think every engineer should be required to totally understand this math. But any engineer using it should understand it. I originally disagreed with you because you claimed that business degrees and economists would use it while engineers make the computers do the work... I called bullshit because I'm an engineer who found it to be useful. (Also, I don't particularly see how this can be applied to business or econ)

>>1449772
All he had to do was substitute a variable into a formula. It's pretty hard to show step by step work for this. Once you realize this is a geometric series, your brain should quickly poop out the answer I gave.

>>1449753

i call bullshit on your being an engineer, due to >>1449753

sorry bro, don't call yourself an engineer until you've earned the credentials!

>>1449823
Okay okay, I'll give you that. I'm majoring in electrical engineering and doing a math minor. I'm going into my third year with a high gpa and ahead of schedule for classes. I'm soon to be an actual engineer.

>>1449831
grats dude on the gpa

i'm an aerospace engineering student with a pretty good gpa lol... calc 2 messed me up

this is why i keep saying fortran though lol

what university are you? illinois? purdue? bradley?

OP, you can delete this thread now that your homework question has been answered

>>1449866
umass lowell

>>1449831
>I'm going into my third year with a high gpa and ahead of schedule for classes.

At my university average GPA going in to the EE major (end of sophomore year) was like 3.6, while average GPA for the last two years in the 300 and 400 level eng classes was 2.3-2.4 and median GPA at graduation was ~3.0. Basically don't get cocky.

>>1449875

iowa state

>>1449902
im going in with 3.85
I took a graduate level (500) signal processing theory class for my math minor and aced it...
i haven't taken any 400 level courses yet, but the A's i've gotten so far are strong/solid grades.... i have no intent to change this, i plan on bulldozing any class that comes my way... i am a cocky motherfucker and proud of it

>>1449928
also, my epeen is fucking huge