Comparison Test

Let $\sum a_k$ and $\sum b_k$ be a Series with Positive terms and suppose $a_1\leq b_1$, $a_2\leq b_2$, ....

1. If the bigger series Converges, then the smaller series also Converges.

2. If the smaller series Diverges, then the bigger series also Diverges.

See also Convergence Tests

References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 280-281, 1985.