1
$\begingroup$

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?

$\endgroup$

2 Answers 2

2
$\begingroup$

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

$\endgroup$
3
  • $\begingroup$ Ah yes, that's very true. $\endgroup$ Oct 2, 2014 at 0:54
  • $\begingroup$ But is there any specific notation? $\endgroup$
    – NeilRoy
    Apr 11, 2015 at 4:08
  • $\begingroup$ 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. $\endgroup$
    – user164587
    Apr 13, 2015 at 15:30
1
$\begingroup$

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 $i \in \{x \in \Bbb N\ |\ x = 2k \wedge k \in \Bbb N\}$".

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.