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Question: How can I simplify this difference ?

Question:How can I simplify this difference ?

YasH 50
simplify
January 24 2014
2

I cannot show that the following two sums(A and B) are equal to each other.

How can I simplify the difference(A-B)?

 

A := sum((-1)^(i-1)*factorial(n0)/(factorial(n1)*(n1+i)^2*factorial(i-1)*factorial(n0-n1-i)), i = 1 .. n0-n1);

 

B := sum(1/(n1+i), i = 1 .. n0-n1);

 

`assuming`([simplify(A-B)], [n0::nonnegint, n1::nonnegint, n1 <= n0]);

 

does not give zero. 

 

The result of a simple test: 


map(simplify, [seq(eval(A-B, n1 = 10), n0 = 20 .. 30)]);
print(`output redirected...`); 

 

is

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

 
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