Re: Can it be done - easily?
- To: mathgroup at smc.vnet.net
- Subject: [mg13242] Re: Can it be done - easily?
- From: Seth Chandler <SChandler at Central.UH.Edu>
- Date: Fri, 17 Jul 1998 03:17:39 -0400
- Organization: University of Houston
- References: <6od25q$hn9@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I'm not sure whether the result qualifies as "simple", but Mathematica
can quickly compute a closed form formula that appears to do what you
want.
In[13]:=
(culhane[x_,{ymin_,ymax_,yinc_}]=FullSimplify[Sum[x/y,{y,ymin,ymax,yinc}]])//
InputForm
Out[13]//InputForm=
(x*(-PolyGamma[0, ymin/yinc] +
PolyGamma[0, 1 + ymin/yinc +
Floor[(ymax - ymin)/yinc]]))/yinc In[14]:=
culhane[10000,{100,1000,100}]//InputForm Out[14]//InputForm=
36905/126
In[15]:=
N[%]
Out[15]=
292.897
Seth J. Chandler
Associate Professor of Law
University of Houston Law Center
Barry Culhane wrote:
> Myself and two workmates are software developers. One guy wanted a
> formula to calculate a result for the following equation...
> Z = sum of X/Y where X is a fixed number, and Y ranges from A-B in
> fixed steps...
> i.e... X=10000 ; Y=100,200,300...1000
> i.e... Z= 10000/100 + 10000/200 + ... 10000/1000 = 292.896
>
> He and I tried to figure out a simple formula to calculate it, but
> couldn't. The third guy said it was *not* *possible* to derive a
> formula - we think he's wrong, but can't prove it. MathCad can solve
> it in the blink of an eye, even if the value of Y ranges from 1 to 1e6
> in steps of 1 !!!
>
> Can anyone come up with a simple formula to give a reasonably accurate
> result? It is too slow to actually divide X by Y for each value of Y
> as there may be 1000 or even 100,000 values of Y.
>
> Thanks in advance...
> > Barry Culhane
> > Schaffner Ltd, Limerick, IRELAND