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How many different values can $\lfloor x \rfloor + \lfloor 2x \rfloor + \lfloor 3x \rfloor +\lfloor 4x \rfloor + \lfloor 5x \rfloor +  \lfloor 6x \rfloor$ take for $0 \leq x \leq 1$?

 

How many different values can    \(\lfloor x \rfloor + \lfloor 2x \rfloor + \lfloor 3x \rfloor +\lfloor 4x \rfloor + \lfloor 5x \rfloor + \lfloor 6x \rfloor\)   take for   \(0 \leq x \leq 1\) ?

 Nov 7, 2021
edited by Alan  Nov 7, 2021

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If n is a positive integer, and \(0 \le x \le 1\) then \(\lfloor nx \rfloor\) can take take the values 0, 1, 2, ... n   i.e it can take n+1 values.

 

This should help you to answer the question.

 Nov 7, 2021

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