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A series evaluation

Victor Moll, Tulane University
Posted 12 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 Keith
David Keith
Posted 12 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
David Keith
David Keith
Posted 12 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
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.
POSTED BY: David Reiss
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

Generally 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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