Element of Leibniz Harmonic Triangle is Sum of Numbers Below

Theorem
The elements in the Leibniz harmonic triangle are the sum of the elements immediately below them.

Proof
By definition of Leibniz harmonic triangle, element $\tuple {n, m}$ is:
 * $\dfrac 1 {\paren {n + 1} \binom n m}$

Thus we have:

Hence the result.