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What is the value of lim[n→∞] (1 - 1/n)ⁿ ?

1. 0
2. e⁻¹
3. e^-n
4. 1

Correct answer: e⁻¹

Solution

As n approaches infinity, the expression (1 - 1/n)ⁿ converges to e⁻¹, which is derived from the limit definition of the exponential function. This limit represents the continuous compounding of a decreasing quantity.

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