state whether the series is convergent or divergent

1) 3 + 12 + 48 + ...
2) 4 + 4/5 + 4/25 + ...

2 answers

#1 surely you don't have to ask about this one -- the terms get ever larger

#2 is simply a geometric series, with |r| < 1, so it converges.
Also, you can tell that the first one is DIVERGENT because the numbers are diverging from one another! In other words, they are getting farther and farther apart

The second one is CONVERGENT because all the numbers are converging to a certain number...in this case they are all getting closer and closer to zero