How to simplify a finite sum plus the next element?

*To*: mathgroup at smc.vnet.net*Subject*: [mg121880] How to simplify a finite sum plus the next element?*From*: Kirill Müller <kirillmueller at gmail.com>*Date*: Thu, 6 Oct 2011 04:18:26 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

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