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A connected graph G is distance-regular if for any vertices x and y of G and any integers i,j=0, 1, ...d (where d is the graph diameter), the number of vertices at distance i from x and distance j from y depends only on i, j, and the graph distance between x and y, independently of the choice of x and y. In particular, a distance-regular graph is a graph for which there exist integers b_i,c_i,i=0,...,d such that for any two vertices x,y in G and distance i=d(x,y), there are exactly c_i...

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This is very interesting! This is why I am obsessed with infinity. It is so strange. Not that strange once you start working with formal definitions. I attached the graphs of the partial sums. In those graphs one can estimate where the limits of those partial sums are.