Re: Can it be done - easily?

*To*: mathgroup at smc.vnet.net*Subject*: [mg13272] Re: Can it be done - easily?*From*: "Allan Hayes" <hay at haystack.demon.cc.uk>*Date*: Fri, 17 Jul 1998 03:18:08 -0400*References*: <6od25q$hn9@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Barry Culhane wrote in message <6od25q$hn9 at smc.vnet.net>... >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 > > Barry: Formula: f[X_,A_,B_,h_]= Sum[X/Y, {Y, A,B,h}] A A -A + B X (-PolyGamma[0, -] + PolyGamma[0, 1 + - + Floor[------]]) h h h ---------------------------------------------------------- h Numerical calculation with formula f[10000,100,1000,100] 36905 ----- 126 N[%] 292.897 Numerical calculation directly with Sum Sum[10000/Y, {Y, 100,1000,100}] 36905 ----- 126 ------------------------------------------------------------- Allan Hayes Training and Consulting Leicester UK http://www.haystack.demon.co.uk hay at haystack.demon.co.uk voice: +44 (0)116 271 4198 fax: +44(0)116 271 8642