When is it allowed to take a constant out of a series?
Suppose we have a series $\sum ca_n$, when can we write it as $c\sum a_n$?
It's pretty obvious when we know beforehand the series converges but what if we're asked to check if the series converges?
Can we take it out and then if it does converge then the operation was legal (like with LHR)?
Lastly, does it matter for diverging series?