Prove that \( \sum_{r=1}^{k}(-3)^{r-1} 3 n_{C_{2 r-1}}=0 \), where \( k=(3 n) / 2 \) and \( n \)...

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Prove that \( \sum_{r=1}^{k}(-3)^{r-1} 3 n_{C_{2 r-1}}=0 \), where \( k=(3 n) / 2 \) and \( n \) is an even positive integer.
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