Re: Can it be done - easily?

*To*: mathgroup at smc.vnet.net*Subject*: [mg13263] Re: Can it be done - easily?*From*: "Stephen P Luttrell" <luttrell at signal.dra.hmg.gb>*Date*: Fri, 17 Jul 1998 03:17:54 -0400*Organization*: Defence Evaluation and Research Agency*References*: <6od25q$hn9@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

>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. Matematica 3 takes the following input Sum[1/n, {n, low, high}] and converts it into the following output PolyGamma[0,1+high]-PolyGamma[0,low] and if you set low=1, high=10 you get 7381/2520 which approximates to 2.92897, which is in agreement with your result. ================================================================= Stephen P Luttrell Signal Processing and Imagery Department DERA Malvern, St.Andrew's Road Malvern, United Kingdom, WR14 3PS +44 (0)1684 894046 (tel) +44 (0)1684 894384 (fax) luttrell at signal.dera.gov.uk (email) http://www.dera.gov.uk/cis5pip/Welcome.html (web)