Today my physics professor briefly skipped over this during a derivation:(adsbygoogle = window.adsbygoogle || []).push({});

We started with

[itex]2 \sum F_{n}(x) = \sum G_{n}(x)[/itex] , summed from n=0 to [itex]\infty[/itex]

which she then concluded

[itex]2F_{n}(x) = G_{n}(x)[/itex]

where F and G are functions of x, and different functions for different values of n. (she was using a generating function)

What proves this is true?

I think this is just equating terms of the sums for values of n, but how do we know this is valid? I provide the counter example:

[itex]\sum x = \sum x^{2} [/itex] for x=0 to [itex]\infty[/itex], which is true

however, equating individual terms is false: x[itex]\neq x^{2}[/itex]

Is there some criteria for equating terms?

thanks

austin

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# Equating terms in summations, simple question!

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