Math Logic

Question :
What are 'Figurate Numbers' ?

Answer :
A figurate number, also (but mostly in texts from the 1500 and 1600s) known as a figural number.
They are just numbers or a series of numbers formed from an arithmetical progression in which the first term is unity and the difference a whole number, by taking the first two, first three, first four, etc., terms and forming a new series, and so on, by forming in the same way.
The numbers of each sequence, when represented by points, can be systematically arranged in various geometrical figures such as triangles, pentagons, tetrahedrons, etc.
The n-th regular r-topic number is given by the formula :
for n >= 2
where, r! is the factorial of r, is a binomial coefficient, and n(r) is the rising factorial.
For Example,
                               
                             
                                      
1                  3                   6
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