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Overview of different strategies for testing convergence of series
The most basic (but often inconclusive) test for divergence is the summand test. Some common series, like infinite geometric series or -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.