Determining Whether the Sum of an Infinite Series is Defined

Determine whether the sum of each infinite series is defined.

1. ⓐ $\text{12}\textrm{ }+\textrm{ }\text{8}\textrm{ }+\textrm{ }\text{4}\textrm{ }+\textrm{ } \ldots$
2. ⓑ $\frac{3}{4} + \frac{1}{2} + \frac{1}{3} + ...$
3. ⓒ $\sum_{k = 1}^{\infty} 27 \cdot \left(\frac{1}{3}\right)^{k}$
4. ⓓ $\sum_{k = 1}^{\infty} 5 k$