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$ \sum_{i=0}^{5}{i^2} = 0^2+1^2+2^2+3^2+4^2+5^2 = 55 $

How to write this Sigma notation only for odd numbers: $ 1^2+3^2+5^2 = 35 $ ?

2 Answers 2

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You could write $ \sum_{i=1}^{3} f(2i-1). $ Otherwise it is allowed to write $ \sum_{1 \leq i\leq 5, i \text{ odd}} f(i). $ (Here in your example $f(i) = i^2$ of course).

So in general whatever condition you have on the index, you can write that underneath the sum. In general you will find some people prefer one thing over another.

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    @Thomas you have typo in your current answer: $ 1 \leq 1\leq 5 $ should probably be $ 1 \leq i\leq 5 $ :)2012-08-29
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Just use the following for any $f(i)$: $\sum_{i=0}^n f(2i+1)$

Edit: Sorry, I somehow mistook the question for "even".

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    With the little caveat that $2i$ is not odd.2012-08-29