Thursday, December 10th, 2009
Overview of the Bounded Monotone Sequence Theorem
Description
A detailed tutorial on the bounded monotone sequence theorem. Step by step tutorial including several examples of the bounded monotone sequence theorem for reference.
Overview
The bounded monotone sequence theorem actually has several parts to it. First, you need to find out if something is bounded above or bounded below. The sequence is bounded above if there exists a real number B such that x sub n is less than or equal to B. The sequence is bounded below if there exists a real number B such that x sub n is greater than or equal to B. If something is a bounded sequence, that means it is bounded both above and below. Absolute values are also very important in determining the bounded sequence. The bounded monotone sequence theorem states that for every bounded monotone sequence x, there is a real number L such that x sub n implies L.
Tags: above, absolute, algebra, below, bounded, boundedness, equal to, greater than, implies, less than, monotone, number, real, sequence, theorem, value
Posted in Algebra | No Comments »
Tuesday, October 6th, 2009
How to Test for Convergence Using the Geometric Series Test
Description
A detailed tutorial on how to test for convergence using the geometric series test. Step by step tutorial including several examples of testing for convergence using the geometric series test for reference.
Overview
A geometric series is a series that maintains a constant ratio between a set of terms. This series is an addition series, and would be expressed as 1/a + 1/2a + 1/4a, extending as far as you wish in either direction. If a series does not have that constant ratio, then it is not a geometric series. The series should converge at one, because as all the numbers are added they get closer and closer to one. The first term of a geometric series is given by a, and the ratio of a geometric series is given by r. If the ratio is less than one, then the geometric series converges to a / (1 – r). If the ratio is greater than or equal to one, then the series diverges. Usually the series will converge, which is why this is considered a test for convergence and not for divergence.
Tags: a, addition, Calculus, converge, convergence, diverge, divergence, equal to, first term, geometric, greater than, less than, Math, notation, r, ratio, series, summation, test
Posted in Calculus | No Comments »
