Flooded Floors

Algebra Level 4

\[ \displaystyle f(x) = \sum_{i=1}^\infty \bigg\lfloor \frac{x + 2^{i-1} } { 2^i } \bigg\rfloor \]

A function \( \displaystyle f : \mathbb{R} \to \mathbb{Z} \) is defined as above. Evaluate: \(\displaystyle f(20.14) \).

Details and Assumptions:

  • \( \displaystyle \lfloor x \rfloor \) denotes the greatest integer less than or equal to \(x\).

  • It is \(20.14\) and not \(2014\).

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