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# 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

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## 1 Answer

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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.

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## Comments

1

Thanks for the fast answer and the fast ticket report!

( 2019-01-22 20:51:07 +0200 )edit

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( 2019-01-23 15:23:38 +0200 )edit

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Asked: 2019-01-22 18:38:13 +0200

Seen: 756 times

Last updated: Jan 22 '19