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Find a closed form equation of the following sequence: ${{0,0,-2,0,4,0,-6,...}}$

I know $1+-1^n$ = 0 if n is odd and 1 if n is even.

However finding alternating signs when plugging in only even numbers seems to be difficult. I.e. finding a g(n) such that g(2)=-2, g(4)=4, g(6)=-6, and so forth.

Alex Georgio
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1 Answers1

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Henning Makholm's comment links to solutions not involving trigonometry. Here is a simple real expression which does:

$$n \cos\left(\frac{n\pi}{2}\right).$$

Henry
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