       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
letter. This will ensure conflicts with built in objects cannot
uppercase letter.

partial sums. With valid values for index1 and the upper limit

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.

```

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