Calculus › Section J · Infinite series › Topic J.6
The ratio and root tests
Factorials and exponentials make comparison awkward, but they shrink in a very regular way. The ratio and root tests measure that shrinkage with a single limit and give the cleanest verdicts in the subject.
In this topic
- Measuring how fast terms shrink
- The ratio test
- Why the ratio test works
- Worked example: powers and factorials
- The root test
- Worked example: a series with mixed signs
- The dead zone at L = 1
- Choosing which test
- Common mistakes to avoid
- Key takeaways
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Standards: 10 (BC)