Chapter 11 - Infinite Sequences and Series - 11.2 Exercises - Page 737: 82

$\Sigma Ca_{n}$ will be divergent.

Note that: $\Sigma ca_{n} = c\Sigma a_{n}$ $\Sigma a_{n}$ is convergent if and only if $\Sigma a_{n}$ is finite. Since $\Sigma a_{n}$ is not finite, $c\Sigma a_{n}$ is also not finite. Hence, $\Sigma ca_{n}$ will be divergent.