Alexc475 said:Homework Statement
Does The series Ʃ (2n)!/(n-1)*3^n converge or diverge?
(Starts at n=2 to infinity )
Homework Equations
The Attempt at a Solution
I tried the ratio test and nth-term test, and ended up with infinity, I'm not sure about it's convergence.
Dick said:If the ratio you get from the ratio test goes to infinity, then the series diverges.
No, if L > 1, it diverges.Alexc475 said:Ohh no wonder. Thank you! I forgot that if L>1 (L being the limit) that it converges
A convergent series is one in which the sum of all the terms in the series approaches a finite number as the number of terms increases. In contrast, a divergent series is one in which the sum of all the terms in the series either approaches infinity or does not approach a finite number.
Determining whether a series converges or diverges is important in understanding the behavior of a given sequence of numbers or values. It can also help in evaluating the accuracy of mathematical models and in making predictions based on the given data.
The most commonly used test for determining convergence or divergence of a series is the Comparison Test. This test involves comparing the given series to a known series with known convergence or divergence properties.
Other commonly used tests for determining convergence or divergence include the Limit Comparison Test, the Ratio Test, the Root Test, and the Integral Test. Each of these tests has its own conditions and criteria for determining convergence or divergence of a series.
No, a series cannot converge and diverge at the same time. A series can either converge or diverge, but not both. If a series satisfies the criteria for both convergence and divergence, then it is known as a conditionally convergent series.