Trying to solve a sum
- To: mathgroup at smc.vnet.net
- Subject: [mg36070] Trying to solve a sum
- From: Constantine <celster at cs.technion.ac.il>
- Date: Thu, 15 Aug 2002 02:36:21 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
I'm trying to solve the following sum:
Sum[ p^(n-k) (1-p)^k Binomial[n, k] * (1+ n -2 k) / (1+n-k), {k, 0,
Ceiling[n/2]} ]
Pls, if anyone knows if that sum has a simple solution, I'll be pleasant
for a hint how to find it.
Thanks in advance.
Constantine.
P.S. The Mathematica produces the following output for this sum:
n 1 1 + n
Out[1]= p ((-) (-1 + 2 p) -
p
1 Ceiling[n/2]
> ((-1 + -) (-1 + p) Gamma[1 + n]
p
n
> ((1 + n) Gamma[n - Ceiling[-]]
2
n n -1 + p
> Hypergeometric2F1[1, -n + Ceiling[-], 2 + Ceiling[-], ------] -
2 2 p
n
> 2 Gamma[1 + n - Ceiling[-]]
2
n n -1 + p
> Hypergeometric2F1[1, 1 - n + Ceiling[-], 2 + Ceiling[-], ------])
2 2 p
n n
> ) / (p Gamma[n - Ceiling[-]] Gamma[1 + n - Ceiling[-]]
2 2
n
> Gamma[2 + Ceiling[-]]))
2
Constantine Elster
Computer Science Dept.
Technion I.I.T.
Office: Taub 411
Tel: +972 4 8294375