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Pascal's Triangle


Each row begins and ends with 1. Each of the other numbers in each row is the sum of the two numbers above it in the previous row. If we label the rows tex2html_wrap_inline1135 , and the entries in each row tex2html_wrap_inline1135 , then entry k of row n equals the binomial coefficient tex2html_wrap_inline1143 . Also, row n gives the coefficients in the expansion of tex2html_wrap_inline1147 :


The sum of the entries in row n is tex2html_wrap_inline1151 . If we divide entry k in row n by tex2html_wrap_inline1151 , then we find the probability of getting exactly k heads when flipping a fair coin n times.

Carl Lee
Wed Apr 21 08:17:28 EDT 1999