Peter Luschny schrieb:   
   >   
   > Correction:   
   > > Still I am worried that Mathematica [Alpha] insists on   
   >      sum(binomial(n-i-1,n-i), i=0..n) = 0.   
   >   
      
   So does Derive 6.10 in fact:   
      
   SUM(COMB(n-i-1,n-i),i,0,n)   
      
   " COMB(m,n) -> COMB(m,m-n) "   
      
   SUM(COMB(n-i-1,-1),i,0,n)   
      
   " If n is a negative integer and m is not, COMB(m,n) -> 0 "   
      
   SUM(0,i,0,n)   
      
   Wait a moment, wait a moment. This rule is misapplied, since n-i-1 is   
   negative for i=n. And COMB(-1,-1) evaluates to 1. Looks like we have   
   caught a real bug in Derive 6.10 here!   
      
   " SUM(F(x),x,a,b) -> SUBST_DIFF(SUM(F(x),x),x,a,b+1) "   
      
   SUBST_DIFF(SUM(0,i),i,0,n+1)   
      
   " SUM(a,x) -> a*x "   
      
   SUBST_DIFF(0,i,0,n+1)   
      
   " SUBST_DIFF(F(x),x,a,b) -> F(b)-F(a) "   
      
   0   
      
   This is consequently wrong, the correct result being 1. Can Alpha   
   display steps for this problem? Is the correspondence accidental?   
      
   Martin.   
      
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