How to sum over half integers? [closed]

I have an expression of the form

Sum[1 + x^n + x^(n^2/2), {n, 0, 10}]

but I want to sum over half integers, that is, I require that $n \in \mathbb{Z}+\frac{1}{2}$ (and later I also want to consider other fractions).

How can I make mathematica, therefore to sum over $\mathbb{Z}+\frac{1}{2}$?

closed as off-topic by m_goldberg, MarcoB, Yves Klett, Bob Hanlon, xzczdJun 16 '16 at 15:33

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• "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – m_goldberg, MarcoB, Yves Klett, Bob Hanlon, xzczd
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• So, Sum[1 + x^n + x^(n^2/2), {n, Range[0, 10] + 1/2}]? – J. M. is away Jun 16 '16 at 10:35
• Oh, is it that simple? Ok thanks! Can instead of Range[..] have a set? Like $\matbb{Z}+1/2?$ – Marion Jun 16 '16 at 10:37

Sum[1 + x^n + x^(n^2/2), {n, 0.5, 10.5}]

• Also Sum[1 + x^n + x^(n^2/2), {n, 1/2, 10 + 1/2}] – Mr.Wizard Jun 16 '16 at 10:41