9: When n grows large, the "−1" part in the ratio can be ignored. Thus the type is

Why zero? ln(2) is a positive number that is smaller than 1, and we know from the limit algebra that such number to infinity yields zero.

So this limit can be done by mere substitution of infinity.

If you are not sure whether the power is indeed definite and yields zero, you can check it by applying the usual procedure for handling general powers: Use the "e to ln" trick, move the exponential out of the limit and use cancelling in the logarithm.

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