## Determine whether an infinite series converges or diverges using the Limit Comparison Test

When it comes to determining whether an infinite series converges (i.e. has a limit) or diverges (i.e. has no limit) there are many tests that can potentially be used. But sometimes a test isn’t applicable, or another test may give an inconclusive result. The limit comparison test can be useful where other tests fail. It doesn’t give a direct result, but allows us to know whether or not two series share the same convergence or divergence. Any questions about this video drop us a message HERE.

## Key Points

The Limit Comparison Test requires a series with a known result to compare to

The comparison series can be deduced from the series to be tested

The Limit Comparison Test is not a convergence or divergence test, it simply tells you whether the two series have the same convergence / divergence result

If the result of the Limit Comparison Test is positive and finite the two series share the same convergence / divergence result

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