Is $ \left\lfloor \frac{n+3}{2} \right\rfloor = \left\lfloor \frac{n}{2} \right\rfloor +1$?

Question

$$ \left\lfloor \frac{n+3}{2} \right\rfloor = \left\lfloor \frac{n}{2} \right\rfloor +1$$ Is it correct? Thanks in advance.

Answer 1

The correct formula is:

$$\left\lfloor \frac{n+3}{2} \right\rfloor=\left\lfloor \frac{n+1}{2} +1 \right\rfloor=\left\lfloor \frac{n+1}{2} \right\rfloor +1 $$

Answer 2

$$ \left\lfloor \frac{n+3}{2} \right\rfloor = \left\lfloor \frac{n+1}{2} +1 \right\rfloor = \left\lfloor \frac{n+1}{2} \right\rfloor +1 $$

so your proposition is true iff $$\left\lfloor \frac{n+1}{2} \right\rfloor = \left\lfloor \frac{n}{2} \right\rfloor $$