Condition for Increasing Binomial Coefficients

Theorem
Let $n \in \Z_{> 0}$ be a (strictly) positive integer.

Let $\dbinom n k$ denote a binomial coefficient for $k \in \N$.

Then:
 * $\dbinom n k < \dbinom n {k + 1} \iff 0 \le k < \dfrac {n - 1} 2$