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How to simplify a finite sum plus the next element?


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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