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.
Andrej Vodopivec
2014-12-21
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.
Andrej Vodopivec
2014-12-21