Verifying that a symbolic expression in two variables is 0.
I want to verify using SAGE that the expression:
( n +1k) 2−n −1−( nk) 2−n+( n k ) 2−n −1+( n k−1) 2−n −1
is identically zero.
The SAGE script for this is:
binomial(n+1,k)2^(-n-1) - binomial(n,k)2^(-n) + binomial(n,k)2^(-n-1) + binomial(n,k-1)2^(-n-1)
I have tried using full_simplify() but it doesn't boil the expression down to zero.
Please help.
Thanks.