Question 57
Suppose that $k$ and $n$ are integers with $0 \leq k \leq n-3$. Prove that
$$
\binom{n}{k},\ \binom{n}{k+1},\ \binom{n}{k+2},\ \binom{n}{k+3}
$$
cannot form an arithmetic progression.
$$
\binom{n}{k},\ \binom{n}{k+1},\ \binom{n}{k+2},\ \binom{n}{k+3}
$$
cannot form an arithmetic progression.