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.