## anonymous 3 years ago Show that if n and k are positive integers, then

1. anonymous

$$\lceil$$ n/k $$\rceil$$ = $$\lfloor$$ (n-1)/k $$\rfloor$$ + 1

2. anonymous

its obvious for $$n\le k$$ because it comes$1=0+1$for $$n>k$$ suppose that $$n=mk+r$$ and $$r<k$$ so we have$\lceil \frac{mk+r}{k} \rceil=m+\lceil \frac{r}{k} \rceil=m+1$and$\lfloor \frac{mk+r-1}{k} \rfloor+1=m+\lfloor \frac{n-1}{k} \rfloor+1=m+0+1=m+1$

3. anonymous

obvious?

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