Simplifying Finite Sums With A Variable # of Terms

*To*: mathgroup at smc.vnet.net*Subject*: [mg21744] Simplifying Finite Sums With A Variable # of Terms*From*: Wretch <arc at astro.columbia.edu>*Date*: Wed, 26 Jan 2000 03:45:43 -0500 (EST)*Organization*: Vacuum*Sender*: owner-wri-mathgroup at wolfram.com

Hello. I'm a user of Mathematica 3.0. A simple example of what I'd like to do is as follows: Suppose you have the finite series S[i_]=Sum[x[k],{k,1,i}] which is equal to x[1]+x[2]+...+x[i], where the total # of terms i is left variable. I'd like mathematica to calculate the difference S[N]-S[N-1] = x[N]-x[0] . I've tried commands like Expand[S[N]-S[N-1]] and Simplify[S[N]-S[N-1]] , but mathematica doesn't simplify it as you would expect. It basically does nothing. I suspect that it needs some sort of clarification as to the nature of N (i.e. it's a positive integer), but I'm not sure. Is there an easy way for me to do what I'd like? Thanks, AC