I'm looking for some help here. I am consistently struggling with operations on irrational / rational numbers and sequence problems and I learn best by understanding the logic behind a particular method. I'm finding that these subjects in particular rely rote memory (or I'm not seeing the logic), so they are giving me some difficulty. I suspect this is my downfall when it comes to these types of questions (especially sequences which seem to rely heavily on memorization of formulas).
So, I'm looking to the community to help me out a bit. Lets break out the two subjects and my specific questions pertaining to each:(Ir)Rational Numers
1). What's the best method to tackle these types of questions? What has worked for you all? Any general best practices?
2). Should I be leveraging scientific notation to render angry, unhappy decimals (
) more approachable (
3). How about roots--what understanding / tricks have you gleaned throughout your study process that has helped you attack these problems with more confidence. I find these to be a complete pain in the behind and often find myself working through an entire PS problem, only to realize that my answer doesn't match up with any of the answer choices.Sequences
1). I think my main issue here is not understanding whats happening behind the formulas. So, I often find myself either trying to memorize a formula I dont fully understand, and as a result not knowing how to apply it effectively. Someone mind giving a theoretical reason that the sequence formulas work the way they do (# of terms, sums of consecutives, sums of evenly spaced sets etc.). I know these are relatively elementary formulas so my question is more along the lines of WHY does it work the way it does not merely what it is, if that makes sense.
2). Again, any best practices you've come across that helped you?
Really appreciate it!