Question: Simplifying this sum over odd integers

Hey,

 

I'm trying to make a sum of only odd numbers regarding 2 functions and I've come up with what I assume is a terrible way to do it...

So basically what I want to write is this:

 


And this should give me something like this:


This works, what I have now. The thing is I need to be able to add and subtract terms in order to compare with other stuff and it just seems so inefficient right now.

 

Thanks in advance!

 

 

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