How can I find the limit of the sequence e^-n?

Thread starter Lance WIlliam
Start date Jul 27, 2008
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Limit Sequence

In summary, a sequence is a list of numbers that follow a specific pattern and each number is called a term. The limit of a sequence is the value that the terms approach as the number of terms increases, denoted by lim n→∞ an. To find the limit, methods such as the squeeze theorem, monotone convergence theorem, or ratio test can be used to evaluate the trend of the sequence. Finding the limit is important for understanding the behavior of the sequence and determining if it is convergent or divergent, with practical applications in fields like physics, engineering, and economics. Some real-life applications of finding the limit include predicting population growth, analyzing financial investments, and determining the efficiency of computer algorithms.

Jul 27, 2008

Lance WIlliam

I believe this sequence converges but how do I Find the Limit of "e^-n"?

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Jul 27, 2008

Defennder

Homework Helper

[tex]e^{-n} = \frac{1}{e^n}[/tex] What happens to the denominator when n approaches infinity?

Jul 27, 2008

Lance WIlliam

It goes to ZERO!
well 1/inifinity is Zero

Related to How can I find the limit of the sequence e^-n?

What is a sequence?

A sequence is a list of numbers that follow a specific pattern, where each number is called a term.

What is the limit of a sequence?

The limit of a sequence is the value that the terms of the sequence approach as the number of terms increases. It is denoted by lim n→∞ an, where n represents the number of terms and a_n represents the nth term of the sequence.

How do you find the limit of a sequence?

To find the limit of a sequence, you can use various methods such as the squeeze theorem, the monotone convergence theorem, or the ratio test. These methods involve evaluating the terms of the sequence and determining the trend or behavior of the sequence as the number of terms increases.

Why is finding the limit of a sequence important?

Finding the limit of a sequence is important because it helps us understand the behavior of the sequence and its terms. It also allows us to determine if the sequence is convergent or divergent, which has practical applications in fields like physics, engineering, and economics.

What are some real-life applications of finding the limit of a sequence?

Some real-life applications of finding the limit of a sequence include predicting the growth or decay of a population, analyzing the stability of a financial investment, and determining the efficiency of a computer algorithm.