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Calc II and difficulty of sequences and series

  1. Jun 27, 2007 #1
    Ok so I am in Calculus II this summer and its pretty easy so far. However, I have heard the hardest part about Calc II is series and seqence. Why so? And what can I do to make it easier on myself? What was your expierence with sequence and series. Thanks in advance.
  2. jcsd
  3. Jun 27, 2007 #2
    its bs, if you've had an easy time so far you'll have an easy time in series and sequences
  4. Jun 27, 2007 #3
    My Real Analysis textbook gave an intuitive description of series/sequences. Understanding that would make what they show you in Calculus 2 a breeze.
  5. Jun 27, 2007 #4
    I found calc II to be difficult for 3 reasons.

    1. The pace that was set. I took it in the summer and the pace was brutal, 4 days a week for 4 hours a day, OUCH!!!

    2. Nothing seemed to build on anything else. You learned a new integration technique, then moved on to a completely different one that has nothing or almost nothing in common (as far as steps taken to solve it goes) with the first one, then moved on to other topics that also had little to do with previous topics. The whole class just seemed to be a mess of subjects that didn't fit in conveniently with any other math class. No other math or engineering class seemed to suffer from this flaw.

    3. The volume of material that needed to be memorized for each test. Unless you’re the type that cheats and puts it into their calculator (when the syllabus specifically says not to), the number of obscure trig identities, trig derivatives, and trig integrals alone could fill a page and a half. Add to that the inverse trig function identities, integrals, and derivatives, the diff EQ stuff, the insane amount of memorizing needed for series and sequences, conics and parametric equations, and you are seriously talking about the final from hell.

    Good luck, I hope it goes well for you. Whatever you do, don't fall behind. Everyday you sit down to study, do 3 or 4 random problems from previous chapters and sections so you don't have to relearn material you haven’t seen for 3 or 4 weeks when test time comes around.
  6. Jun 27, 2007 #5
    Personally, I had an easy time with calcII, but it will depend much more on your professor than calcI did. The concept of infinity, as well as the tests for convergence, do require some intuitivity taht can be learned, but not necessarily memorized. Yes, you can memorize the tests, but you need to know which to use (when you doubt, ratio test!).
    Also, you may at times hear that CalcII is useless whenc ompared to calcI... ignore that. =P
  7. Jun 27, 2007 #6
    Yah but isn't that a grad course or upper level course?

    See I find full memorizing things useless. I can basically derive what I need, I think thats the way to go, I understand it better.
    Wow your lucky , we can't use calculators fpr tests.

    Yah I hear there are tons of rules to test for convergence and divergence.
    But I hear expressing functions as infinite series can be really usefull instead of dreadfull.
  8. Jun 27, 2007 #7
    theres like 5 or 6 that test for convergence and by the end only 3 that matter. and yes series are important.
  9. Jun 27, 2007 #8
    for me, the series and sequences was the easiest part of calc 2. But thats because I learned it for the first time in college and didnt learn it in AP calc. I tried alot harder in college than in AP calc
  10. Jun 28, 2007 #9
    if you do your homework, then it shouldn't be too hard at all.
  11. Jun 28, 2007 #10


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    as courant makes clear there is basically only one general principle for convergence, namely a series converges absoluteky if it is eventually smaller term by term tahn another convergent thing.

    that other thing is almost always either a geometric series, or occasionally an integral. hence the most common test is the ratio test.

    there are a few oddball tests for conditional convergence like the alternating test, and thats about it. the stuff like the root test and so on are seldom used in practice, but of course can occur on exams.

    on the other hand the root method does involve a formula (not a very practical one) for the radius of convergence.

    of course these are the opinions of someone who thinks analysis is hard and not that much fun.
  12. Jun 28, 2007 #11
    I'm currently taking Calc 2 over the summer like you, we just started series/sequences.

    The only real thing that I can see that's hard about series is that yea you have a bunch of "possible" tests that you haveta memorize, as well as results from them, and criteria for each of the test.
    And then! I think the hardest is you go down one road using one test, then you find out it's useless, so start all over try another test, eep that failed too, try another and so forth until you finally get to the result.
    In class we've spent like 30 minutes doing just one problem because we couldn't pick the right test on the first try.

    Just do alot of problems with series, try and get a feel for series on which tests will work and which wont. So in tests you won't waste all of your time doing useless tests.

    Good Luck!
  13. Jun 28, 2007 #12
    this is the truth
  14. Jun 29, 2007 #13
    I took Calc II this past spring semester and, no doubt about it, sequences and series were the hardest concepts for me to understand. I finally got it after a ton of office hours, but I think you just need to do problems. I agree that deciding which test to use can be difficult, but after you do several of them, you notice that one particular test works better for certain kinds of problems than others would. It's all about practice. Don't think of it in terms of memorization, try to understand the concepts and the tests just for the heck of learning it.
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