The ratio test is a method used to determine the convergence or divergence of a series. It involves taking the limit of the absolute value of the ratio of consecutive terms in the series. If the limit is less than 1, the series converges, and if it is greater than 1, the series diverges.
The ratio test is typically used when the terms in a series involve factorials, exponentials, or other complicated functions. It is also useful when dealing with series that involve both positive and negative terms.
No, the ratio test only tells us whether a series converges or diverges. It does not provide the exact value of the sum.
Yes, the ratio test can only be used for series with positive terms. It also may not be applicable for certain series that do not satisfy the necessary conditions for convergence or divergence.
The comparison test is another method used to determine the convergence or divergence of a series. It involves comparing the given series to a known series with known convergence or divergence. The ratio test can be used to prove the convergence or divergence of the known series, which can then be used to determine the convergence or divergence of the given series.