How do you know when to use the ratio test or intregal test. What are the condit
ID: 2863513 • Letter: H
Question
How do you know when to use the ratio test or intregal test. What are the conditions for the ratio test and what should I look for when determining whether or not to use it. The intregal test's conditions include 1. The function is positive. 2. Decreasing. How do you know when to use the ratio test or intregal test. What are the conditions for the ratio test and what should I look for when determining whether or not to use it. The intregal test's conditions include 1. The function is positive. 2. Decreasing. ENCES AND SERIES The Ratio Test tely convergent (i) If lim law/ = L l or lim-1-00, then the series an is divergent. (iii) If lim | +1|-| , the Ratio Test is inconclusive; that is, no conclusion can be drawn about the convergence or divergence of an. PROOF (i) The idea is to compare the given series with a convergent geometric series, SiExplanation / Answer
RATIO TEST-
If an contains factorials then use the Ratio Test. If an involves other products which include
constants raised to a power involving n, then the Ratio Test can be used here too. The Ratio
Test should rarely (as in almost never) be used for rational or algebraic functions involving
polynomials in n or ln(n).
INTEGRAL TEST-
If there is a continuous, positive-valued, decreasing function f(x) such that f(n) = an for
every n, and if, f(x) dx can be integrated, then the integral test can be used. For this
test, it is only important that f(x) is continuous and positive-valued on some interval (c,infinite)
and decreasing on some interval (d,infinite), that is, the function is continuous, positive-valued,
and decreasing from some point on, i.e., not necessarily on (1,infinite). It is quite often the case
that series involving the natural logarithm can be analyzed using this test.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.