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Determine whether the sequence converges or diverges. If it converges, find the limit.$ a_n = 2 + (0.86)^n $

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Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 1

Sequences

Series

Oregon State University

Idaho State University

Boston College

Lectures

01:59

In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence of real numbers is called a finite series. The sum of an infinite sequence of real numbers may or may not have a well-defined sum, and may or may not be equal to the limit of the sequence, if it exists. The study of the sums of infinite sequences is a major area in mathematics known as analysis.

02:28

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first "n" natural numbers (for a finite sequence). A sequence can be thought of as a list of elements with a particular order. Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for series, which are important in differential equations and analysis. Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers.

02:38

Determine whether the sequ…

00:55

01:52

in order to determine whether or not sequence converges or diverges. I need to figure out whether or not the limited n goes to infinity of a M is some finite number. So this is Lim as n goes to infinity of two. Plus you're a point eight six to the end and since you're a point eight six is less than one and absolute value, which is to say that it's trapped between minus one and one. We know that has end goes to infinity. You're a point eight six to the end is going to go to zero, which means that this limit is going to go to two. So the limit exists and the limit is just some finite number. So it converges two, two.

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