I guess those Ramanujan-like infinite series are a bit like trivia questions, right? Does anyone really have an intuition to solve something like that?
Absolutely. Just heading out now, but I'll write out a response for you later on. In short, Being a quant is about either measuring risk, or making money trading. This doesn't test either.
Those are just simple tricks. the first one is 2, the second one, I haven't worked out yet, but it's x where 1/x = 1+x. Just transform those into something with the original in it (square the first, invert the second), then replace the infinite series with the variable you were looking for since you know they'll be equal.
It's just pattern matching. How is this pattern formally defined (for the first problem)? x = sqrt(x + sqrt(x+sqrt(x...))) is informal, so the real definition is a recursion x = sqrt(x + THING), and THING = sqrt(x + THING), which is convenient, because that's just x again. So x = sqrt(x + x) = sqrt(2*x). Oftentimes with mathy stuff (but not always), if you have trouble, right out definitions for the confusing parts and work with that instead, recursing until it makes sense.
Yeah. Those questions seem to be "hey have you seen this cool trick before?" I used to be excited about the American Math Competition back in high school before I realized that memorizing things like the Sophie Germain Identity, the Cauchy-Schwarz inequality, or the Chinese Remainder Theorem would get you through 99% of the problems on the exam. It doesn't test original thinking — it tests if you're "in the know".
As a trading quant starting this Friday, are there any good forums on the net for reading up the soft aspects?
What type of trading? Wilmott forums are okay. Any specific questions?