The Divergence Test is a method used in calculus to determine the convergence or divergence of an infinite series. It involves taking the limit of the terms in the series to see if they approach a finite number or if they diverge to infinity.
The Divergence Test should be used when the terms in an infinite series do not approach zero or if they do not alternate between positive and negative values, making it difficult to use other convergence tests like the Ratio Test or the Alternating Series Test.
To perform the Divergence Test, you must first take the limit of the terms in the series. If the limit is a finite number, then the series is said to converge. If the limit is infinity or negative infinity, then the series is said to diverge. If the limit is inconclusive, then the Divergence Test cannot be used to determine convergence or divergence.
No, the Divergence Test can only be used to determine if a series diverges. If the limit of the terms in the series is a finite number, it does not necessarily mean that the series converges. Other convergence tests must be used to prove convergence.
The Divergence Test and the Integral Test are closely related as they both involve taking a limit to determine convergence or divergence. However, the Integral Test is more versatile and can be used to prove both convergence and divergence, while the Divergence Test can only be used to determine divergence.