It is hard to give advice without knowing what sort of school you are at, whether it is an Ivy league school, European school, or a state college in the US, and what type of course you are in, honors level, math major, etc.
My experience is mostly with average non honors calculus at a state college. Most of my students do not seem to prepare as well as you are trying to do, so maybe my advice is bad for you.
But I think it is actually extremely easy to "read the teachers mind" about what will be on the test, as the teacher almost always tells you in class exactly what to learn for the test. This happens also at top schools. The problem is many students ignore what they are told and do the least amount possible hoping to pass.
So first of all listen closely to your professor. He/she will write the test and hopefully grade it.
As to a source of problems, first of all know how to do every single problem that has been given on homework or worked in class. Also know how to work the examples that are worked out in the book. And know every single problem that has appeared on a previous test from this same instructor in this same course.
It is depressingly easy to stump a class simply by giving the same test over again next time.
The teacher is telling you what to learn by everything he teaches or emphasizes, or assigns on a test or homework or reading assignment. Going into a test without learning the answers to old questions is ignoring the hints you are being given for reading his mind.
In my experience it is also trivially easy to stump most classes simply by giving exactly the same problems that were worked out in examples 1 or 2 in the chapter, or by picking homework problems from the first 10 or 20 at the back of the chapter.
Furthermore almost any standard calculus book, like Stewart, or Edwards and Penney, has a huge array of problems at the back of every chapter, of all levels of difficulty, ranging from trivial computations to theoretical worded questions and proofs.
I would be surprized if your book does not contain such questions, including some more difficult than the standard ones.
It is hard to imagine a class in a typical college today where the student could not get an A+ by preparing by working all (or half of) the problems in the book.
So I suggest studying:
1) what you were told to study.
2) what you were given as homework
3) what you have been tested on before
4) what was worked as examples in the book
5) harder problems at the end of the chapter
On another level of difficulty, when I was a senior level student taking a grad course in real analysis and measure theory, and wanted to be sure I got an A, after learning all the material in our course, (every theorem and every proof), I bought an alternate book on the subject and read that too, and then worked out all the old tests given by the same professor that I could lay hands on.
On the final, sure enough he asked a question that was a standard theorem we had never seen but that was proved in the alternate book, and I got it easily.
I also knew cold the theorems that he had a habit of asking on old tests in prior years.
Even though I had never handed in a single homework all semester, I had a perfect paper and got an A. (Not all professors grade like that, my buddy got a B+ on his final in honors calculus and got a D- for the course. Read the grading policy or ask.)
In another class, I looked up in advanced books the proofs of theorems our teacher had taken for granted in our course, after learning all our own material.
Then on the final, he asked 7 questions and said to work any 4. I worked all 7 and asked him to grade any 4. I also added the extra proof he had left out of the course. I got an A, after getting a D on test 1.
Oh yes after the wakeup call on test 1, I bought a Schaum's outline series problem book and worked as many problems as possible. They seem to have dumbed those books down a bit now though, and they do not contain as many hard problems as before.
So, after doing 1-5 above,
6) go to the library and get alternate books on the subject and read those.
But mainly learn to understand the principle behind the methods you are using to work problems. Do not be like the student in my class, who said he had learned how to maximize the volume of a box with a closed top as I did in class, but he thought it unfair for me to ask on a test for him to maximize the volume of a box with an open top.
That's just plain stupid. Every professor will expect you to apply the ideas you have learned, to related but different situations. Otherwise there is no point taking the course. It is hopeless to learn to solve every problem in the world individually (Ionesco's hopeless student notwithstanding, in "The lesson").
You have to learn general methods that work on whole classes of problems and then be able to work any reasonable problem of that type. Try to see what all problems of a certain type have in common.
After learning to work problems, you should also learn the theory behind the material. This means first of all learning carefully the statements, and understanding the meanings, of the definitions and the theorems.
Learn to use the theorems to prove the important corollaries, and finally learn the proofs of the theorems.
Then practice explaining things to your friends and classmates, and set up a study group to compare levels of understanding and help each other. Trying to do it all alone is usually hard except for unusual students.
On another level, and for future courses, one of my professors said when he was a student he read the material at home before it was sacheduled rto be rpesented in class so he could compare differences of emphasis. Another student I knew sat in on a hard course all year the year BEFORE he took it, and did the work, so when he took it for a grade it was the second time.
I myself sat in on one like that once, but after learning it I did not see the point in sitting through it again, and never took it for credit. I learned more from that course than many others I actually took for credit.
Anyway, you are on the right track, good luck!
The whole point of the question was to check if I could figure out the formula for a series... should've gotten partial points... grumble grumble...
