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MathGroup Archive 1998

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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




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