2014-11-29

euler's number derived from pyramid of additions

2.9: math/euler's number derived from pyramid of additions:
. "( if s#n is the product of the terms in the nth row;
) it shows a pyramid of numbers
but doesn't say how the numbers are generated .
. so there are rows with a list of terms,
and the product means
multiply all numbers in row n to get s#n .
s#(n-1)* s#(n+1) /s#n ^2 = e .
say n=7, s#n = 162000,
s#(n-1) = 2500
s#(n+1) = 26471025 .
(26471025 * 2500) / (162000* 162000) = 2.52
e = 2.7
. I can see how the pyramid is formed:
put 1's down the sides,
then for each adjacent pair in a row,
eg, for 1 2 1
see the pairs (1 2) (2 1)
add the pair and put the result between them
on the row below: 1 3 3 1 .