- #1
Eats Dirt
- 92
- 0
I was just wondering for the limit comparison test does it matter which function is on the top and bottom?
The Limit Comparison Test is a mathematical test used to determine the convergence or divergence of a series. It involves comparing a given series to a known series with a similar behavior.
The Limit Comparison Test works by taking the limit of the ratio between the terms of the given series and the terms of the known series. If the limit is a positive finite number, then both series either converge or diverge. If the limit is zero or infinity, then the behavior of the two series may differ.
The order of the terms in the Limit Comparison Test is crucial as it affects the resulting limit. If the order of the terms is changed, the limit may also change, resulting in a different conclusion about the convergence or divergence of the series.
No, the Limit Comparison Test can only be used for series with positive terms. It also requires the known series to be a convergent series with positive terms.
Yes, there are some limitations to the Limit Comparison Test. It may not work for series with alternating signs or for series with terms that do not have a clear pattern. In these cases, other tests may need to be used to determine the convergence or divergence of the series.