Separating the Even and Odd Portions

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Once separated, the real and imaginary sums must be examined to determine when they are both equal to 0. These sums each regularly alternate between positive and negative terms due to the -1 in the numerator. Further alternating occurs due to the sine and cosine functions. The portion of alternating due to the -1 can be separated by splitting the sums into their even and odd terms. This is shown.

Riemann Hypothesis Proof