       Simplifying Finite Sums With A Variable # of Terms

• To: mathgroup at smc.vnet.net
• Subject: [mg21744] Simplifying Finite Sums With A Variable # of Terms
• From: Wretch <arc at astro.columbia.edu>
• Date: Wed, 26 Jan 2000 03:45:43 -0500 (EST)
• Organization: Vacuum
• Sender: owner-wri-mathgroup at wolfram.com

```Hello.  I'm a user of Mathematica 3.0.  A simple example of
what I'd like to do is as follows:

Suppose you have the finite series

S[i_]=Sum[x[k],{k,1,i}]

which is equal to   x+x+...+x[i], where the total # of
terms i is left variable.

I'd like mathematica to calculate the difference

S[N]-S[N-1] = x[N]-x .

I've tried commands like

Expand[S[N]-S[N-1]]  and  Simplify[S[N]-S[N-1]] ,

but mathematica doesn't simplify it as you would expect.
It basically does nothing.  I suspect that it needs some
sort of clarification as to the nature of N (i.e. it's a
positive integer), but I'm not sure.  Is there an easy
way for me to do what I'd like?

Thanks,

AC

```

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