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

 Mar 31, 2020
 #2
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incorrect....please help! i have one more try

Guest Apr 1, 2020

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