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I'm using Maple 16 to help me in some tedious computations.

I wanted to evaluate the following thing:

$\sum_{i=1}^k\left(\left(\frac{1}{2}\right)^{l+i-1}\cdot\binom{l+i-2}{i-1}\cdot(k-i+2)\right)$

But if I enter the above into Maple, it gets simplified to:

$k+1-l-\frac{\binom{l+k-1}{k}}{2^{k+l}}$

I wanted to prove the equality via induction, but it came up that the two terms are (as far as I can see) something different (just try to set $k=1$).

So: Am I mistaken if I think that the input and output do not represent the same thing or is Maple mistaken for some reason?

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  • $\begingroup$ WA gives a different answer: wolframalpha.com/input/… $\endgroup$
    – lhf
    Jun 24, 2013 at 18:59
  • $\begingroup$ @lhf, yes, I saw that -- while this may be the same (I did not know the Generalized Hypergeometric Function until today). But (secretly) I'm hoping that Maple is right, and the mistake is on my side. $\endgroup$
    – phimuemue
    Jun 24, 2013 at 19:01

1 Answer 1

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It appears to be a bug in Maple.

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