Question

use divergence test to show series diverges
(1 + 1/k ) to the power of k

Answer 1

we can write the series as\[\sum_{k = 1}^{\infty} \left(1 + \frac{1}{k} \right)^k\]then we get\[u_k =\left(1 + \frac{1}{k} \right)^k\]to apply the div. test, first evaluate \[\lim_{k \rightarrow \infty} u_k\]