Answer
Diverges
Work Step by Step
For alternating series $\Sigma_{k=1}^\infty(-1)^k a_k$ (let us consider), to be convergent , we must follow the two conditions such as: a) The magnitude of terms must form a non-increasing sequence.
b) $\lim\limits_{k \to \infty} a_k=0$
We are given that $a_k=(1+\dfrac{1}{k})^k$
In the given sequence, $a_k=(1+\dfrac{1}{k})^k=e$
This implies that the second condition for a alternating series does not satisty.
Thus, the given sequence diverges.
