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Suppose I have a summation like so:

$\sum_{i =0}^n l^i$

Except I don't want to compute for all $0 \leq i \leq n$. I just want to compute it for the arithmetic sequence: $1, 3, 5, 7, 9...$ How do I write this in the summation notation?

Quanquan Liu
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2 Answers2

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Use $2i+1$ instead of $i$ in the expression to be summed.$$\sum_{i=0}^k l^{2i+1}$$ Where $2k+1=n$

user164587
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  • Ah yes, that's very true. – Quanquan Liu Oct 02 '14 at 00:54
  • But is there any specific notation? – NeilRoy Apr 11 '15 at 04:08
  • It depends on the context. $$\sum_{\text{$i$ odd}}l^i$$ is used in some places. $$\sum_{i \in A}l^i \quad (A = {1, 3, 5, \ldots })$$ is also used. The important thing is to be clear. Often this is most easily achieved using words rather than flooding your mathematics with esoteric notation. – user164587 Apr 13 '15 at 15:30
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Like this: $$\sum^n_{i=0}_\text{i is odd} \text{or just} \sum^n_{i=0}_\text{odd}$$ And in general you'd just replace "i is odd" with whatever criteria you have.

Or you could mention it outside the sum. As in, immediately after the sum write "where $i$ is odd" or "where $i \in \{x \in \Bbb N\ |\ x = 2k \wedge k \in \Bbb N\}$".

user180334
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