The ratio test is a mathematical test used to determine the convergence or divergence of a series. It involves taking the limit of the ratio of consecutive terms in the series. If the limit is less than 1, the series converges; if it is greater than 1, the series diverges; and if it is equal to 1, the test is inconclusive.
The ratio test can be used to test for conditional convergence by applying it to the absolute value of the terms in a series. If the absolute value of the terms converges, then the series is absolutely convergent and also conditionally convergent. If the absolute value of the terms diverges, then the series is not conditionally convergent.
The ratio test can only be used for series with positive terms. Additionally, the series must be infinite and the limit of the ratio of consecutive terms must exist.
No, the ratio test can only determine the convergence or divergence of a series, it cannot determine the exact sum. Other tests, such as the geometric series test or telescoping series test, can be used to find the sum of certain types of series.
Yes, the ratio test may not always give a conclusive answer for certain series. In these cases, other tests may need to be used to determine convergence or divergence. Additionally, the ratio test can only be used for series with positive terms and may not work for more complex series.