Definition:Leibniz Harmonic Triangle/Row

From ProofWiki
Jump to navigation Jump to search

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