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 sequences-and-series. 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 sequences-and-series can and usefully distinguished from my proposed summation tag. At present the tag wiki excerpt for summation says:
Questions about evaluating summations, especially finite summations. For infinite series, please consider the (sequences-and-series) tag instead.
and the complete tag wiki entry says:
Use sequences-and-series for sums of infinite series and questions of convergence; use summation for questions about finite sums and simplification of expressions involving sums.
In the day or two since I applied the summation 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 summation 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.
