Determining Whether the Sum of an Infinite Series is Defined

Determine whether the sum of each infinite series is defined.

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

OpenStax, Algebra and Trigonometry 2e · §13.4 Series and Their Notations · Example 8