Re: error with Sum and Infinity

*To*: mathgroup at smc.vnet.net*Subject*: [mg102301] Re: error with Sum and Infinity*From*: Richard Fateman <fateman at cs.berkeley.edu>*Date*: Tue, 4 Aug 2009 04:30:32 -0400 (EDT)*References*: <h56bq2$buv$1@smc.vnet.net>

You've gotten several of the standard work-arounds or excuses, which are really standard issue here. 1. Mathematica is doing the right thing; [by definition] so the mistake is yours. 2. If you computed something else, different from what you wrote, you would get a different answer, but corresponding to what you expected. 3. How can you expect Mathematica to read your mind? Here's one more standard, (from me, anyway). Mathematica has a design problem. The underlying point is that Mathematica is conflating two concepts with the name Sum: A. A loop of finitely many terms evaluated in sequence and adding up the terms. and B. A symbolic calculation based on various combinatorial ideas, the calculus of finite differences, and other systematic simplifications that reduces a summation, either finite or infinite, into a result that does not have any summation notation in it. Like summing arithmetic progressions, geometric progressions, etc (and very advanced etc.). For this second concept to work, the summand must be something that can be suitably manipulated, typically starting as a single algebraic expression. A programming segment, or a pattern match that requires that each value of the index be fed into an evaluator will not, generally work with algorithms for indefinite or definite/infinite summation. Obviously you cannot feed an infinite number of index values into a function and sum up all the terms. A clean solution would be to separate these two concepts: a loop and a symbolic closed-form simplifier for a summation. Or for Mathematica to use the Sum form, but somehow allow you to indicate to the system that you want it evaluated as a loop or simplified to a closed form. RJF

**Follow-Ups**:**Re: error with Sum and Infinity***From:*ADL <alberto.dilullo@tiscali.it>

**Re: Re: error with Sum and Infinity***From:*Daniel Lichtblau <danl@wolfram.com>