Re: sum of binomials .. bug ?
- To: mathgroup at smc.vnet.net
- Subject: [mg70561] Re: sum of binomials .. bug ?
- From: Peter Pein <petsie at dordos.net>
- Date: Thu, 19 Oct 2006 03:23:30 -0400 (EDT)
- References: <eh20si$2ms$1@smc.vnet.net> <eh4oes$885$1@smc.vnet.net>
dimmechan at yahoo.com schrieb: > 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 > This does not explain, why g reduces to the wrong 2^18: In:= Table[Binomial[18,i],{i,0,7}]//Tr Out=63004