How do I add it?

Algebra Level 3

\(f(x) =0-1+2-3+4-5+6-7+8-9+\cdots \begin{cases} -x & \text{if }x \text{ is odd} \\ +x & \text{if }x \text{ is even} \end{cases}\\ p(x) = 1-2+3-4+5-6+7-8+9-10+ \cdots \begin{cases} -x & \text{if }x \text{ is even} \\ +x & \text{if }x \text{ is odd} \end{cases} \)

Two functions \(f(x)\) and \(p(x)\) are defined for all positive integer \(x\) as above. Find \(f(x) + p(x+ 1) \), when \(x\) is odd.

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