Complete question is;
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. (If the quantity diverges, enter DIVERGES.) a_n = (1 + k/n)ⁿ
Answer:
DIVERGES
Step-by-step explanation:
We are given;
a_n = (1 + k/n)ⁿ
Limit of a_n as n tends to infinity is;
This gives;
(Lim n →∞) (1 + k/n)ⁿ
This now gives;
(Lim n →∞) e^(1 + (k/n) - 1)ⁿ
This gives;
(Lim n →∞) e^((k/n))ⁿ
This gives;
(Lim n →∞) e^(k)
Thus;
The sequence a_n = (1 + k/n)ⁿ is divergent
