#2614 simplify_sum returns incorrect result for 1/binomial(n, k) summation

None
closed
nobody
5
2014-12-21
2013-07-22
Robert Dodier
No
load (simplify_sum);
simplify_sum ('sum(1/binomial(n, k), k, 0, n));
 => (n+1)/2^n
%, n=10;
 => 11/1024

That's incorrect:

sum(1/binomial(10, k), k, 0, 10);
 => 1433/630

Thanks to Ed Scheinerman (sage-support newsgroup) for pointing it out.

Discussion

  • Maxima uses the Zeilberger algorithm to attempt to find the closed form. Zeilberger returns something which looks OK but simplify_sum misinterpreters the result.

    I have added a stronger check for zeilberger sums in commit [a04d8e]. Maxima now returns the sum unevaluated.

     

    Related

    Commit: [a04d8e]

    • status: open --> closed