hivesaeed4 said:I have just one question. Suppose the limit comparison test evaluates to infinity. Would it still prove convergence?
The limit comparison test is a method used in calculus to determine the convergence or divergence of a series. It involves comparing the given series to a known series with known convergence properties.
To use the limit comparison test, you first need to find a known series that is either known to converge or diverge. Then, you take the limit of the quotient of the terms of the given series and the known series. If the limit is a finite positive number, then the given series will have the same convergence properties as the known series.
The limit comparison test can only be used on series with positive terms. Additionally, both series must have the same number of terms and the terms must be non-zero. Lastly, the known series must have known convergence properties.
The direct comparison test involves directly comparing the given series to a known series, while the limit comparison test involves taking the limit of the quotient of the terms of the given series and the known series. Additionally, the direct comparison test can only be used when both series have positive terms, while the limit comparison test can also be used when one or both series have alternating terms.
Yes, the limit comparison test can be used to determine both absolute and conditional convergence. If the known series is absolutely convergent, then the given series will also be absolutely convergent. If the known series is conditionally convergent, then the given series may be either conditionally convergent or divergent.