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lgbasallote
Show that if n and k are positive integers, then
\(\lceil\) n/k \(\rceil\) = \(\lfloor\) (n-1)/k \(\rfloor\) + 1
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\[\lfloor \frac{mk+r-1}{k} \rfloor+1=m+\lfloor \frac{n-1}{k} \rfloor+1=m+0+1=m+1\]