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Numerade Educator

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Problem 27 Easy Difficulty

Determine whether the sequence converges or diverges. If it converges, find the limit.
$ a_n = 3^n 7^{-n} $

Answer

Converges

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Video Transcript

to figure out whether or not this sequence converges. There diverges. We need to look at the limit is and goes to infinity of a n And if the limit exists and is finite, then it converges. Otherwise it diverges. So we're looking at freed the end times seven to the minus and seven to the minus and is the same thing as one over seven to the end. Negative exponents make you take the reciprocal. So this is a limit. As in approaches, Infinity of three divided by seven to the end and three over seven is less than one in absolute value. That's what allows us to make this conclusion here. So it does converge and it converges to zero.