I'm trying to figure out how my teacher solved this infinite series, the problem is:

The sum as k = 1 goes to infinity of (1/3)^k,

so the Sequence of terms is: an = (1/3)^n,

and the Sequence of partial sums is S1 = 1/3, S2 = (1/3 + 1/9), S3 = etc.

Then my teacher goes to say that: Lim as n -> Infinity of Sn = 1/2 , and I have no idea how he got that, can anyone help me figure this out?