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Find the limit of the sequence {2ᵉⁿ=1/ᵉⁿ or determine that the sequence diverges.

User Downeyt
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Final answer:

The limit of the sequence is 1.

Step-by-step explanation:

The given sequence is {2ᵉⁿ=1/ᵉⁿ}. To find the limit of the sequence, we can simplify it by using the properties of exponents. Recall that aᵇ/cᵇ = (a/c)ᵇ. Applying this property to the sequence, we have:

{(2/ᵉ)ᵉⁿ}.

Now, as n approaches infinity, the expression (2/ᵉ)ᵉⁿ approaches 1 because the numerator and denominator both converge to 2/ᵉ. Therefore, the limit of the sequence is 1.

User Zoltan Magyar
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