Re: sum of binomials .. bug ?

• To: mathgroup at smc.vnet.net
• Subject: [mg70527] Re: sum of binomials .. bug ?
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Wed, 18 Oct 2006 04:18:32 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <eh20si\$2ms\$1@smc.vnet.net>

```yann_che2 at yahoo.fr wrote:
> Hi everyone,
>
> on Mathematica 5.2 (mac os x), experimenting sums of binomials, i tried
> the following:
>
> In[6]:=   f[k_] := Sum[Binomial[21 - k, i], {i, 0, 10 - k}]
> In[7]:=   x = 3; f[x]
> Out[7]:= 63004
> In[8]:=   Clear[x] ; f[x] /. x -> 3
> Out[8]:= 262144
> In[9]:=   Clear[x] ; f[x]
> Out[9]:= 2^(21-x)
>
>
> does anyone know why Out[7] and Out[8] give different results ? do you
> think it is a bug ? i searched everywhere in the forums but couldn't
> find anything that helped.
> do you have a clue ?
>
> yann
>
No bug here. You are not evaluating the same function. In the first
case, k is replaced by the value 3, then the sum/binomial is evaluated.
In the second case, the sum/binomial is evaluated first, then the value
3 is substituted to k. You can get a consistent result using an
immediate assignment rather than a delayed one.

In[1]:=
f[k_] := Sum[Binomial[21 - k, i], {i, 0, 10 - k}]

In[2]:=
Trace[f[3]]

In[3]:=
Trace[f[x] /. x -> 3]

In[4]:=
Clear[f]
f[k_] = Sum[Binomial[21 - k, i], {i, 0, 10 - k}]

Out[5]=
2^(21 - k)

In[6]:=
f[3]

Out[6]=
262144

In[7]:=
f[x] /. x -> 3

Out[7]=
262144

Regards,
Jean-Marc

```

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