# “summation” tag for finite and formal summations

I often want to improve the tags on questions like "Is it possible to make this expression shorter?". This question asks how to simplify or evaluate the finite sum $$\sum_{i=1}^n\left( 2^{i-1} a_i \sum_{k=0}^{n-i}10^k \binom{n-i}{k} \right)$$

Questions of this type seem to be fairly common, but we don't seem to have a good tag for them. The closest match is . But I understand that tag to be about issues of convergence, since that is why we consider sequences and series together. Naturally there is some overlap, but I think can and usefully distinguished from my proposed tag. At present the tag wiki excerpt for says:

and the complete tag wiki entry says:

Use for sums of infinite series and questions of convergence; use for questions about finite sums and simplification of expressions involving sums.

In the day or two since I applied the tag to that question, it has appeared on several others, all quite appropriately, I think. They concern the sums $\sum_{i=0}^n 3^i$, $\sum_{n=1}^{N} (e^{i\theta})^n$, and $\sum^n_{i=1}2^{i-1}$. I know I have seen many other questions to which I would want to apply the tag. One example is a problem about binomial coefficients sum.

I proposed this in the "tagging" chat room and there was no objection; Martin Sleziak suggested that I bring it up here.

Addendum: Another typical example that just appeared: How can I compute the sum of ${m\over\gcd(m,n)}$?

Another example, where the original poster chose, appropriately, to include the tag: Prove by induction $\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}{4}$ for $n\ge1$

Here's another case where the original poster used the tag themselves: Sum of the Reciprocal of the Difference of Two Squares

Since nobody has objected, and the tag seems to be coming into use, I'm going to start using it regularly, and also gradually start adding it to old questions where appropriate.

• As part of my campaign against uninformative titles, I have retitled the question in your first link. – Gerry Myerson Oct 10 '12 at 2:14

If you're going to bump questions by retagging, maybe consider simultaneously improving the titles also?

For example:

Probably in all of these these cases, the title would benefit from simple copy/pasting the sum into the title.

• I changed a couple of these titles (but didn't touch the tags). – Gerry Myerson Oct 18 '12 at 12:59
• You scared me there for a minute. I thought those were the titles of questions I had retagged without retitling! But none of them are. Yes, I will continue to try to clean up anything I can whenever I can. Thanks for the suggestion. – MJD Oct 18 '12 at 18:52
• Good point, this is in the spirit of Gerry Myerson's post about More informative titles – Martin Sleziak Oct 19 '12 at 8:58