       Re: How to simplify a finite sum plus the next element?

• To: mathgroup at smc.vnet.net
• Subject: [mg121936] Re: How to simplify a finite sum plus the next element?
• From: "Dr. Wolfgang Hintze" <weh at snafu.de>
• Date: Fri, 7 Oct 2011 04:44:09 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j6joce\$m02\$1@smc.vnet.net>

```No solution, but it is sometimes a good idea to use FullForm in order
to see the internal structure of an expression.
In our case

FullForm[Sum[x[i], {i, 1, n}] + x[n + 1]]

Plus[Sum[x[i], List[i, 1, n]], x[Plus[1, n]]]

You can play a little with the internal structure like this:

s = Sum[x[i], {i, 1, n}] + x[n + 1];
ls = List @@ s
{Sum[x[i], {i, 1, n}], x[1 + n]}

ls[[1,1]]
x[i]

ls[[1,2]]
{i, 1, n}

Sum @@ Append[{ls[[1,1]]}, ls[[1,2]] /. n -> n + 1]
Sum[x[i], {i, 1, 1 + n}]

Wolfgang

"Kirill Müller" <kirillmueller at gmail.com> schrieb im Newsbeitrag
news:j6joce\$m02\$1 at smc.vnet.net...

> Hello,
>
> with Mathematica 8, the following formula does not get simplified as
> expected:
>
> FullSimplify[Sum[x[i], {i, 1, n}] + x[n + 1]]
>
> I expect Sum[x[i], {i, 1, n+1}] as output. Instead, the following is
> output:
>
> \!\(
> \*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(n\)]\(x[i]\)\) +
> x[1 + n]
>
> I have already tried various assumptions for FullSimplify -- no luck.
> What am I doing wrong here?
>
>
> Cheers
>
> Kirill
>

```

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