Does the series converge or diverge? if it converges, what is the sum? show your work.

  Converges; -8/3

Step-by-step explanation:

The formula for the sum of a geometric sequence is ...

  S = a1/(1-r)

where a1 is the first term (-4) and r is the common ratio (-1/2). Filling in these values, we get ...

  S = -4/(1 -(-1/2)) = -4(2/3) = -8/3

The series converges to a sum of -8/3.

Third choice, DA = BC

If we knew that DA and BC were the same length, then we could use the ASA congruence property to prove triangles ATD and CTB to be congruent.

Note in the diagram below, segments DA and BC are between the marked angles.