We are in the right year for this! - (2)

Geometry Level 4

\[ \large \sum_{k=1}^{3024} r\left( \cos\left(\frac{k\pi}{2\cdot 3024}\right) \right) \]

We define \(r(x) \) as the nint function, or the nearest integer function. Evaluate the summation above.

Clarification:

  • \(r(x)= \begin{cases} {\left\lceil x \right \rceil \quad , \quad 0.5 < \{ x \} < 1 } \\ {0 \quad\quad , \quad\quad \{ x \} = 0.5 } \\ {\left\lfloor x \right \rfloor\quad , \quad 0 < \{ x \} < 0.5 } \\ { x \quad\quad , \quad\quad\{ x\} = 0 } \end{cases} \)

  • \(\{ x\}\) denote the fractional part of \(x\). That is, \(\{x\} = x - \lfloor x\rfloor \).

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