Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.

3+0.3+0.03+0.003+...

Isn't this converging to 0? If so...its marked wrong by my computer.

The terms converge to zero, but when you see that .... at the end, you also have to look to notice that there is a + + + + + between the terms

Consider this series of partial sums

3
3.3
3.33
3.333
3.3333
3.33333
3.333333
3.3333333
3.33333333
.
.
.

Anyway it converges to 10/3 not 0

There is a difference between sequence and series. The sequence converges to zero yes but thats not what you are looking for. You are looking for where the series converges so the sum of each term in your sequence. Since this is geometric seires we have a formula. If the common ratio is between -1 and 1 then the sum is

(first term) / (1 - (common ratio))

common ratio here is 1/10 since 3*(1/10) = 0.3 and 0.3 * (1/10) - 0.03 and so on
first term is 3

Sum = 3 / (1 - 1/10) = 3 / (9/10) = 3 * (10/9) = 10/3

3+0.3+0.03+0.003+... is infinite GP with A = 3 and CR = 0.1
hence it is convergent and its sum = A / (1 -- CR) = 3 / (1 -- 0.1) = 3/0.9 = 3 1/3