Re: Newbie question: equations with sums.

• To: mathgroup at smc.vnet.net
• Subject: [mg92866] Re: Newbie question: equations with sums.
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Thu, 16 Oct 2008 05:04:26 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <gd4dlf\$bgb\$1@smc.vnet.net>

```Vend wrote:

> FullSimplify[\!\(
> \*UnderoverscriptBox[\(\[Sum]\), \(i = 0\), \(\(-1\) + n\)]i\ f[
>      i]\) == \!\(
> \*UnderoverscriptBox[\(\[Sum]\), \(k = 0\), \(\(-1\) + n\)]k\ f[k]\)]
>
> Evaluates to:
>
> \!\(
> \*UnderoverscriptBox[\(\[Sum]\), \(i = 0\), \(\(-1\) + n\)]i\ f[
>     i]\) == \!\(
> \*UnderoverscriptBox[\(\[Sum]\), \(k = 0\), \(\(-1\) + n\)]k\ f[k]\)
>
> Why doesn't it evaluate to true? Is there a way to make the system
> solve this kind of equations?

Here, what you should test is sameness (===), which is more appropriate
for symbolic expression, rather than equality (==). For instance,

In[1]:= FullSimplify[\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 0\), \(\(-1\) + n\)]\(i\ f[
i]\)\) === \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(k = 0\), \(\(-1\) + n\)]\(k\ f[
k]\)\)]

Out[1]= False

Note the triple equal sign (function SameQ).

The following document might be worth reading:

"What is the difference between =, ==, and === in Mathematica?"
http://support.wolfram.com/mathematica/kernel/features/differentequals.html

Regards,
-- Jean-Marc

```

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