What if on the sum there is a fraction in the limit?
$\sum_{m=k/12}^{k}$ or $\sum_{m=0}^{k/12+1}$
thank you very much!
what type of sequence is used for summing this type of interval?
What if on the sum there is a fraction in the limit?
$\sum_{m=k/12}^{k}$ or $\sum_{m=0}^{k/12+1}$
thank you very much!
what type of sequence is used for summing this type of interval?
In the first case, the sum is over all integers $m$ that are in the closed interval whose endpoints are $\frac{k}{12}$ and $k$.
In the second case, the sum is over all integers $m$ that are in the closed interval whose endpoints are $0$ and $\frac{k}{12} +1$.
(The convoluted language is because in principle $k$ could be negative.)
Remarks: $1$. Part of the convention is that (unless something is said to the contrary) an index called $m$ ranges over integers.
The languages of mathematics, like other human languages, have many such conventions. Often they are not made explicit.
$2$. Probably in principle one should use the appropriate floor or ceiling functions, but they can sometimes interfere with quick understanding, particularly in a subscript or superscript.