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Evaluate the limit as n tends to infinity: (4ⁿ + 5ⁿ)^(1/n).

1. 4
2. 5
3. 5e
4. 4e/5

Correct answer: 5

Solution

(4^n+5^n)^(1/n) = 5*(1+(4/5)^n)^(1/n). As n->infinity, (4/5)^n->0 and the factor ->1, so the limit is 5.

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