On Jan 16, 2008 11:33 AM, Bart Vandewoestyne
<Bart.Vandewoestyne at telenet.be> wrote:
> (%i1) sum( binomial(s, k), k, 1, s); ...
> Apparently, the version of Maxima that I have does not calculate the expression.
By default, Maxima only performs trivial simplifications of sums (e.g.
sum(a,i,1,n) => a*n).
If you turn on simpsum, it does a few more:
sum( binomial(s, k), k, 1, s), simpsum:true;
=> 2^s-1
There are also more powerful summing methods available:
nusum (n^4*4^n/binomial(2*n,n), n, 0, n)
=> 2*(n+1)*(63*n^4+112*n^3+18*n^2-22*n+3)*4^n/(693*binomial(2*n,n))-2/(3*11*7)
Or:
qq: sum (n^4*4^n/binomial(2*n,n), n, 0, n);
(comes back unsimplified)
Try simpsum:
expand(qq,0,0),simpsum:true
(still unsimplified)
Try nusum:
subst(nusum,nounify(sum),qq),eval;
=> 2*(n+1)*(63*n^4+112*n^3+18*n^2-22*n+3)*4^n/(693*binomial(2*n,n))-2/(3*11*7)
You might also want to look at the documentation for Zeilberger and GosperSum.
? zeilberger
=>
-- Function: Zeilberger (<F_{n,k}>, <k>, <n>)
Attempts to compute the indefinite hypergeometric summation of
<F_{n,k}>. ...
---------
-s