Limit Comparison Test

Let $\sum a_k$ and $\sum b_k$ be two Series with Positive terms and suppose

$$\lim_{k\to\infty} {a_k\over b_k} = \rho.$$

If $\rho$ is finite and $\rho > 0$, then the two Series both Converge or Diverge.

See also Convergence Tests