Infinity isn't EXACTLY a number but you can use it like one in many cases.
I've explained "closed form" before. Basically it's a function that returns the same values as a sequence if you pass the natural numbers to it, but it doesn't have any recursion (that is, self-reference) in it.
The ratio is just S
n / S
n-1. For a sequence like this one the ratio is constant across any two consecutive terms. Spoilering the answer:
Without context, I have no idea on Sn = (1/2)(n(2a +(n-1)d)) = n((a1+a2)/2), because I don't know what a, a1, a2, and d are.
What really is a magnetic field?
I mean, you've been studying fields. A magnetic field is a polarized field, just like an electric field. They behave the same way, they're just based on different (but related) underlying forces. "North" in a magnetic field and "positive" in an electric field are analogous.
The compass needle always aligns itself along the field lines, because one end is attracted to the north pole of the magnet and the other end is attracted to the south pole of the magnet. (Of course, that means the pointing end of the compass needle is in fact the compass's SOUTH pole. Don't let that confuse you.)