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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Equating terms in summations, simple question!

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**