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Most people learn the Ratio Test as a formula without understanding the reasoning behind it. Even if you took real analysis, the standard proof might have left you more confused than enlightened.
In this section we will discuss using the Ratio Test to determine if an infinite series converges absolutely or diverges. The Ratio Test can be used on any series, but unfortunately will not always yield a conclusive answer as to whether a series will converge absolutely or diverge. A proof of the Ratio Test is also given.
@GCab That's correct, the ratio test doesn't apply to the harmonic series. But the statement I quoted is still invalid.
Even though Why The Ratio Test Stays Hidden Behind Every Great Math Mystery is complex, it's manageable.
## Why Why The Ratio Test Stays Hidden Behind Every Great Math Mystery Matters
Discover a detailed breakdown of the Ratio Test, including definitions, derivations, and examples, to ace your AP Calculus AB/BC exams.
The ratio test is best used when you have certain elements in the sum. The way to get a feel for this is to build a set of tables containing examples of tests that work as you are working practice problems. This is an extremely powerful technique that will help you really understand infinite series. Here is a list of things to watch for.
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