Series problem w/ questions

For this example, I have many questions about this problem, can someone please answer my questions, and then add anything else about this problem i may need to know.

heres the worked problem: http://img143.imageshack.us/img143/66/untitledfh4.png

questions:

Is this an infinite series?

Why do we select the first part of the Series as Sn? What is Sn?

..I understand that 1/2n is the starting number and the limit for this series,

and that it is greater than any Sn, however, why do we add + 1/2?

(for example, this part: 1/2n >= Sn + 1/2)

..also, then why does the above equation then change to: 1/2n >= n * 1/2n = 1/2

Is this series divergent because the statement: 0 >= 1/2 is false.

Is that the only reason it is divergent?

I would really appreciate it, if someone could answer these questions the best they can.

Thanks for any help here.