hi, Maximers!
I have another summation question: how to compute symbolically
sum(binomal(2*n+1,r)*p^r*(1-p)^(2*n+1-r),r,n+1,2*n+1)-
sum(binomal(2*n-1,r)*p^r*(1-p)^(2*n-1-r),r,n,2*n-)
The answer is binomial(2*n-1,n)*p^n*(1-p)^n*(2*p-1).
(Handwrite trick: write
binomial(2*n+1,r)=binomial(2*n-1,r)+2*binomial(2*n-1,r-1)+binomial(2*n-1,r-2)
and carefully simplify).
It can be verifyed for any given n, but not for general n using Maxima.
I tried direct check with [canadian tree] CAS, the answer was different
so that plotting the difference gave a curve, not a straight line at zero...
Can Zeilberger be applied?
Andrei Zorine
p.s. not GUI, but multiplot3d facility I am missing right now in Maxima.