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# what the heeeckkk

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For every real number $$x$$, let $$\lfloor x\rfloor$$ denote the greatest integer not exceeding $$x$$, and let $$f(x)=\lfloor x\rfloor(2014^{x-\lfloor x\rfloor}-1).$$

The set of all numbers $$x$$ such that $$1\leq x<2014$$  and $$f(x)\leq 1$$  is a union of disjoint intervals. What is the sum of the lengths of those intervals?

Mar 30, 2020

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The sum of the lengths of the intervals is 1/2.

Mar 31, 2020
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