Element of Leibniz Harmonic Triangle as Sum of Elements on Diagonal from Below

Theorem
Consider the Leibniz harmonic triangle:

Let $\tuple {n, m}$ be the element in the $n$th row and $m$th column.

Then:
 * $\tuple {n, m} = \ds \sum_{k \mathop \ge 0} \tuple {n + 1 + k, m + k}$

Proof
Taking $r \to \infty$ in Lemma 2: