RE: Simplifying Finite Sums With A Variable # of Terms

*To*: mathgroup at smc.vnet.net*Subject*: [mg21793] RE: [mg21744] Simplifying Finite Sums With A Variable # of Terms*From*: "Harvey P. Dale" <hpd1 at is2.nyu.edu>*Date*: Thu, 27 Jan 2000 22:57:31 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Here's one way to do what I think you want to do. I'll show the steps separately, and then put them all together. First, generate the series of partial sums: In[1]:= FoldList[Plus, 0, Range[10]] Out[1]= {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55} Second, partition the list into groups of adjacent terms: In[2]:= Partition[%, 2, 1] Out[2]= {{0, 1}, {1, 3}, {3, 6}, {6, 10}, {10, 15}, {15, 21}, {21, 28}, {28, 36}, {36, 45}, {45, 55}} Third, map the difference between adjacent terms into the list: In[3]:= {#[[1]], #[[2]], #[[2]] - #[[1]]} & /@ % Out[3]= {{0, 1, 1}, {1, 3, 2}, {3, 6, 3}, {6, 10, 4}, {10, 15, 5}, {15, 21, 6}, {21, 28, 7}, {28, 36, 8}, {36, 45, 9}, {45, 55, 10}} Fourth, transpose the result and select the list of differences: In[4]:= Transpose[%][[3]] Out[4]= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Putting this all together: Transpose[{#[[1]], #[[2]], #[[2]] - #[[1]]} & /@ Partition[FoldList[Plus, 0, Range[10]],2,1]][[3]] Hope that helps. Harvey -----Original Message----- 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