- #1
bfusco
- 128
- 1
Homework Statement
Ʃ[(-1)^n (cosn)^2]/√n
The Attempt at a Solution
i don't have the slightest clue where to start
JG89 said:The initial value for n doesn't matter. It's presumably not zero.
Convergence and divergence are terms used in mathematics to describe the behavior of a series. A series is said to converge if the terms in the series approach a finite limit as the number of terms increases, and it is said to diverge if the terms in the series do not approach a finite limit.
There are several tests that can be used to determine the convergence or divergence of a series. These include the ratio test, the comparison test, the integral test, and the root test. Each test has its own conditions and limitations, so it is important to understand the requirements for each test before using them.
Convergence and divergence are important concepts in mathematics because they allow us to understand the behavior of infinite series. They are used in various mathematical applications, such as in calculus, probability, and statistics, and play a crucial role in understanding the convergence of numerical methods used in solving equations.
No, a series can either be convergent or divergent, but not both. If a series converges, it means that the terms in the series approach a finite limit, and if a series diverges, it means that the terms in the series do not approach a finite limit.
Absolute convergence and conditional convergence are two types of convergence that apply to series with both positive and negative terms. Absolute convergence occurs when the absolute values of the terms in the series converge, while conditional convergence occurs when the series converges, but the absolute values of the terms do not converge.