# Thread: Need Reference to Math Info ( Series and Sequences )

1. ## Need Reference to Math Info ( Series and Sequences )

Hey.. finals coming up :P i was wondering if anyone here know where i could get a site that lists all the types of series and how to test for their convergence/divergance.

Also, is there any site that you know of that gives you sum tips on finding the general term of a sequence. thanx in advance.

EDIT: Not doing Fourier series, and i alrdy chked yahoo, can';t find nothing worth my time :P

2. thanx.

3. Correct me if I am wrong but are there really only 2 ways to check for convergence? They are just a proccess you go through to find them. If you can do some you can pretty much do them all....

Fourier series convergence is another animal totally. I don't like it one bit.

4. Not doing fourier, that comes next semester.. But what we aare doing now goes like this.

1. We are given a Sum from 1 to infin of the term An( n is subscript ).

2. The queston wants us to discuss the if this term diverges, converges, if it does converge, does it converge absolutly or conditionally.

We were introduced to several tests in class that we use to evaluate this general term ( most use limits, and depending on what the limit of the general term is, we get if it diverges or converges. ) The tests we used in class were..
(i) The nth term test
(ii) The geometric series test
(iii) The integral test
(iv) The comparison tests
(v) The alternating series
(vi) The ratio test
(vii) The root test

There may be a way, or test that works for all general terms.. but we were not introduced to it.. ( profs would do that wouldn;t they :P ) How would you approach a question that asked us to evaluate the general term? let me look up an example for ya.

5. When I get home I will give you the 2 tests that work every time (I think because that's the only 2 we ever used on any question. Both could be used one is easier then the other in some cases though). I'm at school right now so... when I get home... I'm actually studing fourier transform right now :P

6. haha, sucks for you :P im studying mechanics.. finding the centroids of volumes of different density. Not to fun if you ask me :P

7. Hey GP.. I was wondering.. could you give me a "physical" description of what it actually means when a series "converges"?

That is sumthing ive never really understood.. and hence this is the only part of the math course i do not understand fully. i could memorise all the tests n such and apply them no prob.. but that is pretty much useless once the final exam is over..

So If possible.. what does it mean when a series converges? graphical representation.. anything.

8. Well the physical representation or graphical rep is kind of weird. In the end you just want to know of the sumation of the signal (or equation or series or what ever you want to call it) over all possible values (-iv inf to inf) is bounded. If there is a DC term in your signal then the summation of the signal will diverge -> summation will go to inf. Because as you go to inf you will always continue to sum that DC term over and over and over. If not then as you sum (or in the continuous version integrate) the sum will be bounded by some constand B. All those tests just try to tell you if this "B" exsists. The only place you use this stuff is really in geometric series convergence...

9. i think i get what your saying.. meh.. i'll jus have to work on it :\

10. a(n-1)d.

Where:
a = first term
n = nth term
d = difference between terms.

This is for a numerical series i think. Can't remember the one for a geometric series.

11. buff, i just stumbled across that site like earlier today haha, it has lots of infomation on it thanx.

12. umm I think he means physical like a real world representation

Like if you drop a ball and it always comes back to half it's original height, it will bounce an infinite amount of times, but over a finite time period.

The sequence would look like H+2H/2+2h/4+2h/8.......

If you need help with problems I can most likely help you pretty easily, I rock at series.

13. Originally posted by nejar462
umm I think he means physical like a real world representation

Like if you drop a ball and it always comes back to half it's original height, it will bounce an infinite amount of times, but over a finite time period.

The sequence would look like H+2H/2+2h/4+2h/8.......

If you need help with problems I can most likely help you pretty easily, I rock at series.
Yeah.. thats what i mean.. but i still can't picture it.. you plot a graph of bounce vs time.. and you say time is limited.. then how can the bounce be infinite? it will only keep bouncing increasingly small intervals until it reaches that limited time.. bleh! i hate this stuff :P

The biggest problem i have with them, is recognizing which "general series form" the question is.. you know what i mean? I have trouble simplifying the expression down to a recognizable form

Here is an example, what method would you use to reduce this?

SUM from n=(4 to infinity) of the term ( n-3 ) / ( n^3 - 3n^2 - 4n + 12 )

14. umm, that'll definetly converge, is that all you're asked to do, because I don't have the knowledge to sum that, unless you want to use the integral test, which'll only give u bounds...

just consider the largest term of N, and use that

15. divide everything by the highest order of n which is n^3 and you will clearly see it goes to 0.

16. since as n aproaches infinity the n^3 term dominates the expression.

17. you can also use sequences and series for compound interest equations.

18. I don't know of any sites, but a great maths book is Mathematical Methods in the Physical Sciences by Boas. There is a great chapter on series in there. It was kind of the maths bible when I was doing stuff like that in college.

19. Math test is over.. It went Semi Fine, sum weird questions, but overall not bad. I will not post until Dec. 13th

This week is crazy

20. Originally Posted by defcon
Math test is over.. It went Semi Fine, sum weird questions, but overall not bad. I will not post until Dec. 13th

This week is crazy

Yeah I got destroyed on my Linear signals exam.

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