Can we pull out a constant of a divergent series?

I know that if a series converges, the following applies:

$$
\sum_{n=i}^\infty c a_n = c \sum_{n=i}^\infty a_n
$$

However, I can't seem to find any info on whether this holds for diverging series as well. The property is often mentioned together with this one, of which I know it does not apply to divergent series:

$$
\sum_{n=i}^\infty a_n + b_n= \sum_{n=i}^\infty a_n + \sum_{n=i}^\infty b_n
$$

This makes me think the first property might require the same condition, but I'm not sure.