Question 52
Prove the identity:
$$
\sum_{j=0}^{n} \left\{ \binom{3n+2-j}{j} 2^j - \binom{3n+1-j}{j-1} 2^{j-1} \right\} = 2^{3n},
$$
where the second term on the left side is to be interpreted as $0$ for $j = 0$.
$$
\sum_{j=0}^{n} \left\{ \binom{3n+2-j}{j} 2^j - \binom{3n+1-j}{j-1} 2^{j-1} \right\} = 2^{3n},
$$
where the second term on the left side is to be interpreted as $0$ for $j = 0$.