I'm planning to write a math olympiad in a couple of months (4-5), and am just really trying to get the preparation in. I'm a fairly good math student (did ok in math, not an A+, but I got an A so my fundamentals are good I think). I was just wondering if someone could suggest some excellent books that are good for beginners and will open my mind to questions involving concepts such as:
-Proving arithmetic progressions that meet some sort of criteria think these kinds of questions (Proving a set of numbers has arithmetic progressions of arbitrary length, but none infinite)
etc... and in general constructing proofs about sequences/series, that sort of thing.
That would be really awesome. I'm kind of scrambling all over the place to find the approximate syllabus for these Olympiad questions, so guidance in finding resources to learn would be great.