the Leibniz Harmonic Triangle (binomial coefficients)

These are formed by doing combination formulas,

where the first row is index 1,

and the first column of each row is index 1 shown below

Leibniz Formula

L(r,c) =

1

r(_{r - 1}C_{c - 1})

Leibniz Table

1/1

1/2

1/2

1/3

1/6

1/3

1/4

1/12

1/12

1/4

1/5

1/20

1/30

1/20

1/5

1/6

1/30

1/60

1/60

1/30

1/6

1/7

1/42

1/105

1/140

1/105

1/42

1/7

1/8

1/56

1/168

1/280

1/280

1/168

1/56

1/8

How does the Pascal-Floyd-Leibniz Triangle Calculator work?

Free Pascal-Floyd-Leibniz Triangle Calculator - This generates the first (n) rows of the following triangles:
Pascal‘s Triangle
Leibniz‘s Harmonic Triangle
Floyd‘s Triangle This calculator has 1 input.

What 2 formulas are used for the Pascal-Floyd-Leibniz Triangle Calculator?

Floyds Triangle is built using natural numbers Sum Row(n) for Floyds = n(n^{2} + 1)/2

What 4 concepts are covered in the Pascal-Floyd-Leibniz Triangle Calculator?

combination

a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter _{n}P_{r} = n!/r!(n - r)!

leibnizs triangle

a triangular arrangement of unit fractions in which the outermost diagonals consist of the reciprocals of the row numbers and each inner cell is the cell diagonally above and to the left minus the cell to the left.

pascals triangle

a triangular array of the binomial coefficients

triangle

a flat geometric figure that has three sides and three angles

Example calculations for the Pascal-Floyd-Leibniz Triangle Calculator