Talk:Convergent Series can be Added Term by Term

I see that the name is a bit vague ("can be" is vague indeed). How about "Convergent Series added Term by Term Converges to their Sum"? Well, "their sum" is a bit ambiguous, since the value of a series is also a "sum". A very explicit title would be "Two Convergent Series added Term by Term is a Series Converging to the Sum of their Sums". Isn't that a mouthful? My first thought was to state the equality the other way around: "A Series Split Termwise into Two Convergent Series Converges to their Sum". Perhaps better? ––St.nerol (talk) 14:31, 18 April 2022 (UTC)

Best approach would be consistent with the existing such results for sequences, with a view towards constructing a comprehensive set of such results in the same vein: Combination Theorem for Series in the same way as Combination Theorem for Sequences. If you're not up to addressing this, then the maintenance tag will remain in place until someone does. --prime mover (talk) 14:37, 18 April 2022 (UTC)

Right. It could be "Sum Rule for Convergent Series" then. But I'm not up to doing more of these at the moment! ––St.nerol (talk) 15:39, 18 April 2022 (UTC)