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I've recently been introduced to sigma notation, and I'm aware that $\sum (f(x) + g(x)) = \sum f(x) + \sum g(x)$. Though what is $\sum f(x)g(x)=?$

Can this be simplified similar to above? Furthermore, if I have $\sum (f(x))^2$ can it be simplified further?

I've asked my teacher, though they don't know. I've also looked online, though have been unsuccessful in finding any information on it.

Thanks

frog1944
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1 Answers1

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When the functions $f(x)$ and $g(x)$ are multiplied together in the summand as you have written: $\sum f(x)g(x)$ there is no rule that applies to simplify it unlike the former case where you distributed them over addition. The same reasoning applies to $\sum (f(x))^2$ since this is still just two functions multiplied together: $\sum f(x)f(x)$.

This probably explains why your teacher doesn't know either.

BLAZE
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