Final answer:
The Ratio Test is used in mathematics to assess the convergence of infinite series; especially relevant to sequences with factorials, exponentials, or variable growth. In health sciences, ratios define mixture proportions, differing from the mathematical application.
Step-by-step explanation:
The Ratio Test is frequently used in mathematics to determine the convergence or divergence of an infinite series, especially when series terms involve factorials, exponentials, or other functions where the growth rate of terms significantly varies.
The Ratio Test involves taking the limit of the absolute value of the ratio of consecutive terms in the series, that is, |a_{n+1} / a_n|. If the limit is less than 1, the series converges; if it is greater than 1, the series diverges; and if the limit equals 1, the test is inconclusive.
In the health sciences, ratio tests are mentioned in the context of mixture solutions, where they are expressed as proportions, such as a 1:1000 solution. However, when discussing series convergence, we typically refer to the mathematical Ratio Test rather than these mixture proportions.