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Leibniz's triangle

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

 


Explanation

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) + ···

 


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