# 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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