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?
It appears to be a bug in Maple.