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Prove that sum(r=1)^(k) (-3)^(r-1) ""^(3...

Prove that `sum_(r=1)^(k) (-3)^(r-1) ""^(3n)C_(2r-1) = 0` , where `k = 3n//2` and n is an even integer.

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To prove that \[ \sum_{r=1}^{k} (-3)^{r-1} \binom{3n}{2r-1} = 0 \] where \( k = \frac{3n}{2} \) and \( n \) is an even integer, we can follow these steps: ...
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