# For what values of #r# does the sequence #a_n = (nr)^n# converge ?

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The sequence (a_n = (nr)^n) converges if and only if (|nr| < 1). Therefore, it converges for values of (r) such that (-\frac{1}{n} < r < \frac{1}{n}), excluding (r = 0).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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