Great Wall Of Cosine (The answer's Over 9000)!

Calculus Level 5

Given that the maximum value of:

\[f(x)=\lim _{ n\rightarrow \infty }{ \left( \sum _{ k=0 }^{ x }{ { \cos { \left( k° \right) } }^{ n } } \right) } \] is \(A\), and given that

  • \(x\) ranges over the positive integers such that \(0\le x\le 360\)

  • \(n\) is an odd number even as it approaches \(\infty \)

  • that the sum of all the possible values of \(x\) which would give \(\left(f(x)=A\right)\) is \(B\)

    Find \(\left\lfloor 100(A+B) \right\rfloor \)


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