[seqfan] Re: Mathematica's or my err?

[David W. Cantrell]

It's an error present in Mathematica versions 5.1 and 6.0, at least.

I'm not running the most recent version of Mathematica and so I 
checked with Wolfram Alpha. Asked to compute 

Sum[(1/i)*Binomial[2n-i-1,i-1],{i,1,n}]

it returns

(-1 + Hypergeometric2F1[1/2 - n, -n, 1 - 2 n, -4])/(2 n)

That seems to be a correct answer, and so I would guess that the 
current version of Mathematica does not have the error you noticed.

David


----- Original Message ----- 
From: "zak seidov" <zakseidov at yahoo.com>
To: "seqfaneu" <seqfan at seqfan.eu>
Sent: Saturday, April 24, 2010 12:05
Subject: [seqfan] Mathematica's or my err?


> Dear seqfans with Mathematica
> (or other tools?!),
> anyone may wish to check this strange result:
>
> FullSimplify[Sum[(1/i)*Binomial[2n-i-1,i-1],{i,1,n}]] =
> (2^(-1 - 2*n)*(-4^n + (1 + Sqrt[5])^(2*n)))/n
>
> I use M 5.1.
> Thanks, Zak
>
>
>
>
>
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