13: The algebra of infinity gives

This indeterminate ratio could be handled by l'Hospital's rule, but that would require first pulling logarithm out of the limit so that the limit applies only to the ratio, only then applying l'Hospital's rule and the outcome is rather unpleasant (try it).

A far better approach is to use the approach from polynomials at infinity, since when n is large, then the "−1" under the root can be ignored and the ratio is approximately n/n = 1. To prove it the best way is to factor out the dominant power in the numerator.

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