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Binomial Coefficient Equivalency

  • #1
Find an expression that is identical to [itex]\sum_{k=0}^n \binom{3n}{3k}[/itex]

According to Wolfram, the correct solution to this is: [itex] \frac{1}{3} \left(2(-1)^n + 8^n\right)[/itex]

But I'm not sure which identities of the binomial coefficient I'm supposed to use to prove this. Can anyone give me some direction?

Thanks!
 

Answers and Replies

  • #2
Does nobody have any ideas? I was wondering if it were possible to confirm Wolfram's answer via induction, but expanding the resulting binomial coefficients fron the [itex]n-1[/itex] to the [itex]n[/itex] case is proving to be fairly difficult. Any help is appreciated.
 

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