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Prove that sum(k=0)^(n) (-1)^(k).""^(3n...

Prove that ` sum_(k=0)^(n) (-1)^(k).""^(3n)C_(k) = (-1)^(n). ""^(3n-1)C_(n)`

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To prove the identity \[ \sum_{k=0}^{n} (-1)^{k} \binom{3n}{k} = (-1)^{n} \binom{3n-1}{n}, \] we will follow a step-by-step approach. ...
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