Re: sum of binomials .. bug ?

• To: mathgroup at smc.vnet.net
• Subject: [mg70500] Re: sum of binomials .. bug ?
• From: dimmechan at yahoo.com
• Date: Wed, 18 Oct 2006 04:16:38 -0400 (EDT)
• References: <eh20si\$2ms\$1@smc.vnet.net>

```There is not a bug at all.
Be more careful before accused Mathematica of bugging.
I do not say that it is panacea but Most of the cases when
someone thinks he encountered a bug the fault is due to him.

Any way for your case the following will demonstrate that indded
there is no bug. (Everything is in InputForm).

Quit

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

Trace[f[3], Binomial]
{{HoldForm[Binomial[18, 0]], HoldForm[1]}, {HoldForm[Binomial[18, 1]],
HoldForm[18]}, {HoldForm[Binomial[18, 2]], HoldForm[153]},
{HoldForm[Binomial[18, 3]], HoldForm[816]}, {HoldForm[Binomial[18, 4]],

HoldForm[3060]}, {HoldForm[Binomial[18, 5]], HoldForm[8568]},
{HoldForm[Binomial[18, 6]], HoldForm[18564]},
{HoldForm[Binomial[18, 7]], HoldForm[31824]}}

Trace[f[x] /. x -> 3]

{{HoldForm[f[x]], HoldForm[Sum[Binomial[21 - x, i], {i, 0, 10 - x}]],
HoldForm[2^(21 - x)]}, HoldForm[2^(21 - x) /. x -> 3], HoldForm[2^(21
- 3)],
{{HoldForm[-3], HoldForm[-3]}, HoldForm[21 - 3], HoldForm[18]},
HoldForm[2^18],
HoldForm[262144]}

g[k_] = Sum[Binomial[21 - k, i], {i, 0, 10 - k}]
2^(21 - k)

g[3]
262144

g[x] /. x -> 3
262144

```

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