# Bug in computing sum (of binomials) One gets a wrong output when running the following command:

sage: sum(binomial(1,n),n,0,oo)
3


The output should be $2$ instead of $3$. Compare:

sage: sum(binomial(1,n),n,0,oo,algorithm="sympy")
2

edit retag close merge delete

Sort by » oldest newest most voted This bug originates from Maxima: if you evaluate

sum(binomial(1,n),n,0,oo)


then it returns

from sage.calculus.calculus import symbolic_sum
symbolic_sum(binomial(1,n),n,0,oo)


which calls

maxima_calculus.sr_sum(binomial(1,n),n,0,oo)


which returns

from sage.interfaces.maxima_lib import max_to_sr, maxima_eval, max_ratsimp, max_simplify_sum, max_sum, sr_to_max
args = [binomial(1,n), n, 0, oo]
max_to_sr(maxima_eval([[max_ratsimp],[[max_simplify_sum],([max_sum],[sr_to_max(SR(a)) for a in args])]]))


Indeed we can see the bug in Maxima's simplify_sum:

(%i1) load("simplify_sum");
(%i2) simplify_sum(sum(binomial(1,n),n,0,inf));
(%o2)                                  3


I reported it upstream at Maxima, simplify_sum(sum(binomial(1,n),n,0,inf)) gives 3 instead of 2, and it is now tracked as trac ticket #27092.

more

1

Thanks for the fast answer and the fast ticket report!

If an answer solves your question, please accept it by clicking the "accept" button (the one with a check mark, at the top left of the answer).

This will mark the question as solved in the Ask Sage's list of questions, as well as in lists of questions related to a particular query or keyword.