# Sequence Homework Help: Find the Limit of a Converging Sequence

• jacoleen
In summary, a converging sequence is a sequence of numbers that approaches a specific limit as the number of terms in the sequence increases. To find the limit of a converging sequence, the limit formula can be used. This formula states that the limit is equal to the previous term plus the common difference between terms, multiplied by the number of terms in the sequence. A converging sequence differs from a diverging sequence in that it approaches a limit while a diverging sequence does not have a limit. A converging sequence can only have one limit, which can be approached from either direction. Real-world applications of converging sequences can be found in physics, finance, and computer science.
jacoleen

## Homework Statement

Determine whether the following sequence converges or diverges. If converges, find the limit:

a = [1+(2/n)]^n

## The Attempt at a Solution

I thought the limit would be one as inside the brackets at infinity it would be 1^n which would equal 1

*the answer given at the back of the book is e^2

## What is a converging sequence?

A converging sequence is a sequence of numbers that approaches a specific limit as the number of terms in the sequence increases. This means that as the sequence continues, the terms get closer and closer to the limit value without ever reaching it.

## How do I find the limit of a converging sequence?

To find the limit of a converging sequence, you can use a formula called the limit formula. This formula states that the limit of a sequence is equal to the limit of the previous term plus the common difference between terms, multiplied by the number of terms in the sequence. The more terms you have in the sequence, the closer your estimated limit will be to the actual limit.

## What is the difference between a converging sequence and a diverging sequence?

A converging sequence approaches a specific limit as the number of terms increases, while a diverging sequence does not have a limit and the terms continue to get farther and farther away from each other as the sequence continues.

## Can a converging sequence have more than one limit?

No, a converging sequence can only have one limit. This limit can be approached from either direction, but the sequence will always approach the same value as the number of terms increases.

## What are some real-world applications of converging sequences?

Converging sequences are used in many fields of science and technology, including physics, finance, and computer science. In physics, they are used to model the behavior of particles in motion. In finance, they are used to calculate compound interest and predict stock market trends. In computer science, they are used in algorithms and data compression techniques.

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