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Prove that if m is a positive integer and x is a real
Chapter 2, Problem 27E(choose chapter or problem)
Prove that if \(m\) is a positive integer and \(x\) is a real number, then
\(\lfloor m x\rfloor=\lfloor x\rfloor &+\left\lfloor x+\frac{1}{m}\right\rfloor+\left\lfloor x+\frac{2}{m}\right\rfloor+\cdots +\left\lfloor x+\frac{m-1}{m}\right\rfloor\).
Equation Transcription:
Text Transcription:
[mx]=[x]+[x+1/m]+[x+2/m]++[x+m-1/m]
m
x
Questions & Answers
QUESTION:
Prove that if \(m\) is a positive integer and \(x\) is a real number, then
\(\lfloor m x\rfloor=\lfloor x\rfloor &+\left\lfloor x+\frac{1}{m}\right\rfloor+\left\lfloor x+\frac{2}{m}\right\rfloor+\cdots +\left\lfloor x+\frac{m-1}{m}\right\rfloor\).
Equation Transcription:
Text Transcription:
[mx]=[x]+[x+1/m]+[x+2/m]++[x+m-1/m]
m
x
ANSWER:
SOLUTION
Step 1
We have to prove that
That is we have to prove,
……..(1)