Hello all,
I am using Mathematica version 7 and would like to ask a question to those using newer versions.
The expression
t1 = Sum[ j Binomial[A, j] Binomial[B, n - j], {j, 0, n}]
can be calculated by pencil and paper giving as result
A Binomial[ A + B - 1, n - 1]
while evaluating the expression for t1 (on my system) yields
-(((-1)^n A (-1 - A - B + n)!)/((-A - B)! (-1 + n)!))
Feeding numbers to it gives
In[58]:= A Binomial[ A + B - 1, n - 1] /. A -> 7 /. B -> 5 /. n -> 4
Out[58]= 1155
but
In[60]:= t1 /. A -> 7 /. B -> 5 /. n -> 4
Out[60]= 0
Obviously something is severely wrong!
The same thing comes along with
In[15]:= t2 = Sum[ j^2 Binomial[A, j] Binomial[B, n - j], {j, 0, n}]
Out[15]= ((-1)^n A (B - n + A n) (-1 - A - B + n)!)/((1 - A - B)! (-1 + n)!)
which is evaluated by the paper and pencil method to
A (A - 1 + (A + B - 1)/(n - 1)) Binomial[A + B - 2, n - 2]
with striking differences when you feed numbers in.
What do the newer versions of Mma say to this?
Regards, Hans Dolhaine
