In ℝ^k, if ∑ ||x_n|| converges absolutely, does ∑ x

In ℝ^k, if ∑ ||x_n|| converges absolutely, does ∑ x_n converge?

A Yes, absolute convergence implies convergence

B No, absolute convergence does not imply convergence

C Only if x_n ≥ 0 componentwise

D Only if the terms are monotone

Correct Answer: Option A