Convergence Tests

Divergence Test

Statement

Comment

then may or may not converge.
Hint: Use the behavior of the limit, how goes to zero, as a clue!

Comparison Test

Statement

be series with positive terms such that:

converges then converges.
Similarly, diverges, then diverges.

Comment

While this test is the foundation of most other tests, use it as a last resort. Other tests are often easier to apply.