$$\sum_{i=0}^{\left\lfloor\frac{n}2\right\rfloor}f(i)+\sum_{j=\left\lfloor\frac{n}2\right\rfloor+1}^nf(i)$$
Hello, I am working on a problem which contains the above term.
When a sigma notation summation has a fractional end value (e.g., $n/2$, where n is odd) do we evaluate it until the the $n/2-1$ term, or do we evaluate it to the $n/2+1$ term? Or something completely different?
Example: If n were 5, would we evaluate two terms, or three terms, or something else?
There is not a fractional end value, because $\lfloor x\rfloor$ means $x$ rounded down to the nearest integer, hence $\lfloor x\rfloor\in\mathbb{Z}$ is always an integer.