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Determine whether the sequence converges or diverges. If it converges, find the limit.$ \left \{ \frac {\ln n}{\ln 2n} \right \} $

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Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 1

Sequences

Series

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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.

01:52

Determine whether the sequ…

01:43

02:38

02:11

for this problem. We're looking at a n equals natural log of n divided by natural log of two in So one thing you, Khun Dio, when you're looking at the limit as in goes to infinity is you could apply low petals rule to this Another thing that you could do It would be to write this as natural log of n divided by natural log of in plus natural log of two. Hello. Patel's rule would work fun, rewriting and in this way would also work well. And now when you do limit as n goes to infinity of Anne, you could do it. But I do know Patel's rule or written in this way we could also do the trick where we look at the term that's going to infinity, the fastest and the denominator, and divide the top on the bottom by that term so we can divide the top on the bottom by natural log in. And as n goes to infinity, this term is going to go to zero. We just have one over one, which is one. So the sequence does converge. It converges to one

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