Leibniz''s triangle

< 1 2 3 4 5 6 7 8 9 10 11 12 >

The harmonic triangle of Leibniz shows the Leibniz numbers in Pascal's triangle.

A number is the sum of the number to the left and right there just below. You see it by 1/20 = 1/60 + 1/30.

The outermost diagonal is the harmonic series

1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + ···

The second diagonal is the Leibniz series

1/(1 × 2) + 1/(2 × 3) + 1/(3 × 4) + 1/(4 × 5) + ···

The German mathematician Gottfried Leibniz (1646 - 1716) developed this triangle.