Definition:Leibniz Harmonic Triangle/Row
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Definition
Consider the Leibniz harmonic triangle:
- $\begin{array}{r|rrrrrr}
n & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline 0 & \frac 1 1 \\ 1 & \frac 1 2 & \frac 1 2 \\ 2 & \frac 1 3 & \frac 1 6 & \frac 1 3 \\ 3 & \frac 1 4 & \frac 1 {12} & \frac 1 {12} & \frac 1 4 \\ 4 & \frac 1 5 & \frac 1 {20} & \frac 1 {30} & \frac 1 {20} & \frac 1 5 \\ 5 & \frac 1 6 & \frac 1 {30} & \frac 1 {60} & \frac 1 {60} & \frac 1 {30} & \frac 1 6 \\ \end{array}$
Each of the horizontal lines of numbers corresponding to a given $n$ is known as the $n$th row of Leibniz harmonic triangle.
Hence the top row, containing a single $1$, is identified as the zeroth row, or row $0$.
Also see
Sources
- Weisstein, Eric W. "Leibniz Harmonic Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LeibnizHarmonicTriangle.html