Euler project 12: triangle number

I am writing this only because I find these simple math trick is like magic.
Triangle number is ones composed by adding previous number together, like the additive analog of factorial number: Tn = 1 + 2 + 3 + ... + n. Now it asks what is the first triangle number with more than 500 divisors?

There are several ways to generate a triangle number. One is use the plain equation to sum up; other one is clearly use the sum-up equation Tn = n*(n-1)/2. However, since what we basically need here is to iterate all triangle numbers starts with 1 (or some bigger yet still small number), I add a step every time using Tn = Tn-1 + n. I think latter two should be mostly at the same speed.

Another thing is to find the number of divisors for a number. This is just iterate from 1 to sqrt(n), according to many math properties. Also since divisors appear in pairs, one might add two every time it finds a fit one if one uses this method; but minus one if the divisor it finds happens to be the sqrt(n).

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