Question

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.) an

Answer 1

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