Question

Show that if n and k are positive integers, then

Answer 1

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

Answer 2

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\[\lfloor \frac{mk+r-1}{k} \rfloor+1=m+\lfloor \frac{n-1}{k} \rfloor+1=m+0+1=m+1\]

Answer 3

obvious?