StevenXClontz’s avatarStevenXClontz’s Twitter Archive—№ 1,999

    1. Assume f→∞,g→∞,f/g→0. Must (f/g)/(f'/g') converge to nonzero? If so, then L'Hopital can be used to find series convergence. #calculus
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    Turns out, nope. Counterexample: math.stackexchange.com/a/77057/86887
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      @StevenXClontz Another great example from christophernight.net: f=x,g=e^x. In this case both series converge, though.
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      1. …in reply to @StevenXClontz
        Suppose f→∞,g→∞,f/g→0. Can (f/g)/(f'/g')→0? If not, then it's possible Σ(f/g) diverges whenever Σ(f'/g') does.
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