Category:Element of Leibniz Harmonic Triangle as Sum of Elements on Diagonal from Below
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This category contains pages concerning Element of Leibniz Harmonic Triangle as Sum of Elements on Diagonal from Below:
Consider the Leibniz harmonic triangle:
- $\begin{array}{r|rrrrrr}
n & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline 0 & \frac 1 1 \\ 1 & \frac 1 2 & \frac 1 2 \\ 2 & \frac 1 3 & \frac 1 6 & \frac 1 3 \\ 3 & \frac 1 4 & \frac 1 {12} & \frac 1 {12} & \frac 1 4 \\ 4 & \frac 1 5 & \frac 1 {20} & \frac 1 {30} & \frac 1 {20} & \frac 1 5 \\ 5 & \frac 1 6 & \frac 1 {30} & \frac 1 {60} & \frac 1 {60} & \frac 1 {30} & \frac 1 6 \\ \end{array}$
Let $\tuple {n, m}$ be the element in the $n$th row and $m$th column.
Then:
- $\tuple {n, m} = \ds \sum_{k \mathop \ge 0} \tuple {n + 1 + k, m + k}$
Pages in category "Element of Leibniz Harmonic Triangle as Sum of Elements on Diagonal from Below"
The following 3 pages are in this category, out of 3 total.