In $\sum_{n=1}^{\left\lfloor \delta/2 \right\rfloor}$, what does ${\left\lfloor \delta/2 \right\rfloor}$ mean?

Question

What does the symbol ${\left\lfloor \delta/2 \right\rfloor}$ mean here? $$\sum_{n=1}^{\left\lfloor \delta/2 \right\rfloor}$$

Any reference on understanding its usage in binomial theorem would be helpful.

Answer 1

It is the floor function applied to $\frac{\delta}{2}$. If $\delta$ is odd then $\left\lfloor\frac{\delta}{2}\right\rfloor=\frac{\delta-1}{2}$; if $\delta$ is even, then $\left\lfloor\frac{\delta}{2}\right\rfloor=\frac{\delta}{2}$. As for how it relates to the binomial theorem, we'd have to see the full expression you're considering in order to determine that.