# Homework Help: Binomial Coefficient Equivalency

1. Apr 4, 2013

### TranscendArcu

Find an expression that is identical to $\sum_{k=0}^n \binom{3n}{3k}$

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

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!

2. Apr 5, 2013

### TranscendArcu

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 $n-1$ to the $n$ case is proving to be fairly difficult. Any help is appreciated.