Re: maximum of a series

*To*: mathgroup at smc.vnet.net*Subject*: [mg114144] Re: maximum of a series*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Thu, 25 Nov 2010 05:56:52 -0500 (EST)

On 11/24/10 at 7:00 AM, olfa.mraihi at yahoo.fr (olfa) wrote: >On 20 nov, 12:10, Bill Rowe <readn... at sbcglobal.net> wrote: >>On 11/19/10 at 5:08 AM, olfa.mra... at yahoo.fr (olfa) wrote: >>>how can I represent for example themaximumof the summations >>>:sum[a[k],{k,i,j}] where j varies from i to n? >>I will take your "represent" as "determine". That is I take your >>question to be how to find themaximumof the partial sums that are >>(in principle) formed when evaluating >>Sum[a[k],{k,i,j}] >>If I have this correct, I suggest >>Max@Accumulate@Table[a[k], {k,i,j}] >>Evaluation of Sum only returns the final sum not any of the >>intermediate sums (which Mathematica may not actually compute). >>I've used Table to create each of the a[k] terms and Accumulate to >>compute the partial sums. >what I need exactly is to solve this system for m using reduce, >Max[m, s + Max[Table[Sum[a[index2], {index2, i, index1}], {index1, >i, N}]]] == >Max[m, t + Max[Table[Sum[a[index2], {index2, j, index1}], {index1, >j, N}]]] >but I have the error: iterator in Table does not have appropriate >bounds You cannot use N as the maximum value for Table. N has built in meaning and cannot be used as a symbol taking a numeric value. Try replacing N with a lower case n and see if this fixes the problem. You would be well advised to never use an uppercase letters as a variable name. Even better, don't have any variable/symbol/function you create start with an uppercase letter. This will ensure conflicts with built in objects cannot occur since the names of all built-in objects start with an uppercase letter. Additionally, your code is inefficient. It repeatedly computes partial sums. With valid values for index1 and the upper limit n, your code Table[Sum[a[index2], {index2, i, index1}], {index1, i, n}] can be replaced with Accumulate@Table[a[index2], {index2, i, n}] or even better if a is a function with the attribute listable Accumulate[a[Range[i,n]] Here, I make the assumption a[n] is what Mathematica interprets it to be, i.e., the function a evaluated at n.