I want to verify using SAGE that the expression:
${~~n~+1\choose k}~2^{-n~-1} - {~n\choose k}~2^{-n} + {~n\choose ~k~}~2^{-n~-1} + {~n \choose ~k-1}~2^{-n~~-1}$
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.
