/sci/ - Science & Math

How the FUCK do I determine a sequence's convergence? As in how do I execute it? I know the definitions, |xn - limit| < ε for n>=N, etc., but I just can't ever really move forward from that whenever I have to do an actual exercise. How do I approach these exercises, what's the actual process to doing them? Please provide examples. 4th time I'm in some sort of basic Maths course in Uni and every time I get hung up on this shit and there goes the whole semester ;_;