20: The l'Hospital rule way should lead to

If you tried to work with powers, you should have found the dominant terms 2ⁿ in the numerator and n² in the denominator. Since "exponentials beat powers", the guess should be that the ratio goes to infinity. Proof: Factoring leads to

To prove that the first fraction goes to infinity is done by twice using l'Hospital's rule almost exactly as in the direct calculation, so here the powers approach is longer, you may as well apply the l'Hospital rule to the whole fraction.

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