Summary of Strategies for Testing Series Convergence - Expii
The most basic (but often inconclusive) test for divergence is the summand test. Some common series, like infinite geometric series or \(p\)-series, have easy, fully conclusive convergence tests. For more complicated series, you may need to use other methods, such as modifying a finite number of terms or comparing to a simpler series or integral. If you have an alternating series in particular, the alternating series test may come in handy.