       RE: question on Sum over selected integers

• To: mathgroup at smc.vnet.net
• Subject: [mg43858] RE: [mg43833] question on Sum over selected integers
• From: "David Park" <djmp at earthlink.net>
• Date: Thu, 9 Oct 2003 01:54:31 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Ghassan,

Suppose we want to sum the function f over selected integers.

f[x_] := x^2

Let's do a smaller range from 1 to 10 for the example. Here the sum is
developed in steps.
1) Generate the full range of integers
2) Take the complement with the missing integers
3) Map the function onto the list
4) Apply Plus to convert the List to a sum

Range
Complement[%, {2, 6, 8}]
f /@ %
Plus @@ %
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
{1, 3, 4, 5, 7, 9, 10}
{1, 9, 16, 25, 49, 81, 100}
281

We can encapsulate all this into a single function.

specialsum[f_, missing_, n_] := Plus @@ f /@ Complement[Range[n], missing]

specialsum[f, {2, 6, 8}, 10]
281

David Park

From: Ghassan Shahin [mailto:ghassans at bethlehem.edu]
To: mathgroup at smc.vnet.net

Hi..
I have a simple question..
i want to use mathematica for sums..but i need to sum from 1 to 100
except same integer numbers, say 2,6,8..what is the code for such a