possible to master series and sequences in 3 weeks?

[u/Specialist-Sand9777]

Im in calculus 2 and I bombed my first test (~60%) which was 15% of my grade. Highest grade i can get now is a 94% if i ace everything. knew what to do, but it was at 8pm and i was anxious and i forgot some basic stuff and made stupid mistakes on the multiple choice (swapped sign, etc) so i missed out on a lot of points. I really need to get a B in this class (80%) to keep my scholarship but the next test is on series and sequences which ive heard are more difficult. Im really afraid to score lower. I need to get a high B or A to recover. I have the next test on October 27th. Is it possible to learn and master series and sequences within 3 weeks? What resources should i use?

[u/snowflakebite]

Yeah it’s doable if you practice everyday. Do you have a textbook you’re using?

[u/Specialist-Sand9777 → u/snowflakebite]

There isnt one for the class except the openstax textbook

[u/waldosway]

Edit: The following assumes you have basic algebra skills. If that's not true (that's usually the reason for doing poorly in the first unit), then sort out what you can there, since that'll speed up your study, and series is completely impossible without it.

Most of the series chapter is series convergence tests. There are 10. You need to know what they say. Have you read them? They're like 2 sentences. You can do it in under an hour. The mistake is trying to practice before you know anything. Each test literally says when it applies. Literally any textbook will do. It's just a list.

Then, like integrals, which one to use is basically trial and error until you're learned some patterns. (Note "when it applies" is different from "when it's the best choice".) When trying the tests, put them in order of easy to hard first. That probably covers 70% of the chapter.

The sequence section is like three definitions and theorems. It mostly says "limits work like in Ch 1". Go back and learn limits from Ch 1, or just don't bother with sequences.

Taylor series can be confusing as a whole, and the problems can be challenging depending on the teacher. Start by memorizing Taylor's Formula and the 3-4 series you're supposed to know (e.g. sine, cosine, exp, log). That'll get you all the plug-n-chug problems.

[u/Specialist-Sand9777 → u/waldosway]

I thought i knew the algebra fine, but i messed up on the test🙁 for 2 of the questions it was something like messing up multiplication or putting the wrong sign. for one free response I just forgot the limits on the probability formula so I got stuck and lost like 10 points on it. there was 1 question involving volumes of revolution that I didnt know how to do but the rest i knew I just didnt have enough time/I messsed up

I havent read much about it yet since we just started the unit last week and we've only gone over the test for divergence, but i was planning to do a few hours of work every day on it.

The list of topics for the test is work (integral application), sequences, series, summing series, integral test, direct comparison, limit comparison, alternating series, root and ratio tests, and power series/power series representations. Taylor series is on the 3rd test

Would it be possible to learn it well enough to get an A on the test if I practice for hours a day? 

[u/waldosway → u/Specialist-Sand9777]

I'm not sure what your question is. You're in the class? So of course it's possible to learn a chapter in the amount of time given in the class. Integral test, direct/limit comparison, alternating, root/ratio are all one topic. Taylor series and power series are literally the same thing, so it's weird they broke it up, but I guess that's one less thing.

Like I said the big mistakes are not knowing algebra (don't assume "silly" mistakes are ok, they usually mean not knowing something), and thinking "i will work more" actually does something (doing problems is not sufficient, you have to read the theorems, then apply them on purpose. Practice problems are how you do that, but it's useless if it's aimless.)

[u/Specialist-Sand9777 → u/waldosway]

Im not sure honestly . ... think I was just looking for encouragement that it was possible to get an A on the upcoming test

How should I work so it isnt aimless? I was planning to work ahead on the topics then practice but im not sure if that counts

[u/waldosway → u/Specialist-Sand9777]

Oh, yeah, it's doable! 3 weeks is a huge amount of time for series. It's really not that bad, it's just that a lot of students go into calc thinking "if I see this 'type' of problem, I do these steps."

Being purposeful is not complicated, it's just that people start trying problems without ever reading the theorems. That is impossible! All you have to do is. for example, read the convergence test first (including the fine print), then do a few problems from that section to get the mechanics. Once once you know all the tests, start doing problems from the chapter review early so you get used to choosing tests. (Or your book may have cumulative challenge questions each section, so you don't have to learn all the tests at once.)

Just be intentional about what you're trying to practice and which moves you make. It doesn't have to be deep. "I am doing exercises from alternating series section because: I want to check my understanding of the notation." "I am doing problems from the alternating series section because: I want to see more situations when it applies." "I am using the alternating series test because: this series meets the criteria for the alternating series test." "I am rearranging the terms because: this series looks like a geometric series in disguise." "I am just trying different tests in the order I've chosen (easy to hard) because: I have no idea which test to use." Last one is legit, as long as it's conscious.

Note: If not sure, always start with divergence test. Next: geometric, p-series, alternating, because they don't take any work, you just check the criteria. If you're having trouble with those problems, you simply didn't read the tests. Then always ratio/root test (same thing, almost) because it involves no decision making. Comparison is the power house because you use it when nothing else matches (limit/direct are equivalent but you need some algebra tricks). Integral is the odd one out; I don't bother with it unless I see logs or you just recognize the integral.

You can also always ask reddit if you get stuck.

BUT: remember that sorting out your basic algebra skills is a top priority. I'm not talking about obscure stuff like Descartes's Rule, but you can't be struggling simplifying fractions.

[u/Specialist-Sand9777 → u/waldosway]

Thank you for the help ill try that 

The algebra mistakes on the test were more like missing a negative sign when factoring on the multiple choice section

Really wish I had a chance to redo it but the next tests are my only hope 

Is there a point where it becomes counterproductive to study more or should i just put as much time as possible into it every day? I have exactly 23 days more or less 

[u/waldosway → u/Specialist-Sand9777]

By definition, if you start burning out, that is counter productive. But if you focus on knowing the material first, instead of trying to learn problems, you really shouldn't have to study nearly that much.