Let's say we have the statement [itex]\sum^{\infty}_{0}f(x)=\frac{\sum^{\infty}_{0}g(x)}{\sum^{\infty}_{0}h(x)}[/itex] does this imply that(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int^{\infty}_{0}f(x)=\frac{\int^{\infty}_{0}g(x)}{\int^{\infty}_{0}h(x)}[/itex]?

Also if [itex]\sum^{\infty}_{0}f(x)=\sum^{\infty}_{0}g(x)[/itex] does this imply that [itex]f(x)=g(x)[/itex], or just that f(x)~g(x) (asymptotically equivalent)?

Thanks.

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# Properties of Summations and Integrals question

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