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Re: General form of a summation as a function of 2 variables

  • To: mathgroup at smc.vnet.net
  • Subject: [mg97420] Re: [mg97376] General form of a summation as a function of 2 variables
  • From: "David Park" <djmpark at comcast.net>
  • Date: Fri, 13 Mar 2009 04:47:12 -0500 (EST)
  • References: <20111798.1236844319845.JavaMail.root@m02>

In Mathematica, if you evaluate the following statement you obtain the
general answer for all n.

Sum[k/n, {k, 0, n}]
(1 + n)/2


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/  

From: David Diez [mailto:david at stat.ucla.edu] 


My goal is to have a general form of a summation that is a function of two
variables, and would like to see if Mathematica can be used to determine the
general form.

For example, with a single variable, is there a way to get Mathematica to
take

sum_{k=0}^n (k/n)

and determine the general formula for the sum (as a function of 'n') is
(n+1)/2?

The problem I am looking at is a bit more complicated (incorporates a five
factorials) and is a function of two variables, m and n. I have never
programmed in Mathematica (but do have programming experience in a few
languages), and any direction on what resources or functions are appropriate
for this sort of problem would be greatly appreciated. If this sort of thing
can only be done in one variable, that would also be very useful since I'll
just look at a particular case (when the two variables are equal: m=n).

Thanks much for any help,
David




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