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GROUPS:
Mathematics
Mathematica
Symbolic Computations
A series evaluation
Victor Moll
Victor Moll, Tulane University
Posted
11 years ago
I have used Mathematica 9.0 to evaluate the series
Sum[2^n/CatalanNumber,{n,0,Infinity}]
that appeared as a question in an issue of the
American Mathematical Monthly.
I need to know how Mathematica finds the sum.
Thanks.
POSTED BY:
Victor Moll
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David Reiss
David Reiss, Scientific Arts
Posted
11 years ago
Sum[2^n/CatalanNumber,{n,0,Infinity}]
does not converge. Is that the expression that you were intending to write?
You also may want to read this:
https://reference.wolfram.com/mathematica/tutorial/WhyYouDoNotUsuallyNeedToKnowAboutInternals.html
G
enerally Mathematica uses a variety fo algorithms to get to its answers  many of which are not the way a person computing by hand will approach a problem.
(I see from your website that you most certainly know this! So, I am leaving this comment in for others that may stumble on this question... ;) )
POSTED BY:
David Reiss
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David Keith
David Keith
Posted
11 years ago
He means
In[87]:= Sum[2^n/CatalanNumber[n], {n, 0, Infinity}]
Out[87]= 1/2 (10 + 3 \[Pi])
The editor chopped the square brackets.
But how MMA does it, that I don't know.
Best,
David
POSTED BY:
David Keith
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David Reiss
David Reiss, Scientific Arts
Posted
11 years ago
Yes, I just realized that the expression was the one you mentioned. If one does not use the code formatting tools things like that happen. For example here I write
f[x]
but in line it comes out as f even though I actually did type it in with the brackets and the x. It's a bug in the community.wolfram.com interface.
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David Reiss
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David Keith
David Keith
Posted
11 years ago
Yes  I suspect the editor is looking for formatting codes of some kind. But it would be better I think to just have a vanilla flavored editor for text.
POSTED BY:
David Keith
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