Finite Set

Author

Eric W. Weisstein
January 18, 2009

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Logic/FiniteSet.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/FiniteSet.html.

©2009 Wolfram Research, Inc. except for portions noted otherwise

Sums

(∑_(k=0)^n)(Binomial[n, k])==(2^n)

Sum[Binomial[n,k],{k,0,n}]

Product

(((∏_j^k)(j-k+n))/(k!))==(Binomial[n, k])

((Product[n-k+j,{j,k}])/(k!))//FullSimplify

FullSimplify[((Pochhammer[1-k+n,k])/(k!)),(k|n)∈Integers&&k>0&&n>0]

Table[((Pochhammer[1-k+n,k])/(k!))-Binomial[n,k],{n,0,3},{k,0,n}]