Series Tests - Weebly
Series Tests
1. The test for divergence: If [pic] then the series [pic]diverges. Always use this test first.
2. The integral test: If [pic] then the series[pic] converges. If [pic] then the series [pic]diverges. Use this if it is easy to integrate [pic].
3. The p-series test. If [pic] use this test. If [pic] the series [pic]diverges. If [pic] the series [pic]converges.
4. The comparison test. If [pic] is a known convergent series and [pic] < [pic] then the series converges. If [pic] is a known divergent series and [pic] > [pic] then the series diverges. If [pic] can be compared to a series that is known to converge or diverge then use this test.
5. Limit comparison test. If [pic] where C is a finite number and C > 0 then both series converge or diverge. Use this if you can compare [pic] to a series but you can’t tell if the series is greater or smaller than the compared series.
6. Alternating series test. If [pic](an alternating series) where [pic] and [pic] then the series converges. Use this for alternating series.
7. Ratio Test. If [pic] the series is absolutely convergent. If [pic] the series is divergent. If [pic] then you need more tests. Use this test if the others aren’t obvious or if [pic] contains a mixture of factorials, geometric, and p-series.
8. [pic]: If [pic] then the series is absolutely convergent. If [pic] then the series diverges. Use this if your general term is in the form of [pic].
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