$ \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 $ ?
$ \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 $ ?
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.
Just use the following for any $f(i)$: $\sum_{i=0}^n f(2i+1)$
Edit: Sorry, I somehow mistook the question for "even".