What is the General Term for an Expansion?

Thread starter c00ky
Start date Aug 13, 2006
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Expansion General Term

In summary, a series is a sequence of terms that are added together to form a sum. It can be either finite or infinite, with a finite series having a limited number of terms and an infinite series having an unlimited number of terms. A series is represented using sigma notation, with the variable below the sigma representing the starting term and the variable above the sigma representing the ending term. A geometric expansion is a type of series where each term is found by multiplying the previous term by a constant number, called the common ratio. To find the sum of a series, a specific formula can be used depending on the type of series, such as the formula Sn = n/2(a1 + an) for finite arithmetic series and taking the limit for

Aug 13, 2006

c00ky

Hi guys, can anybody solve the following problem?

http://putfile.com/pic.php?pic=main/8/22412435578.jpg&s=f10"

Last edited by a moderator: Apr 22, 2017

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Aug 13, 2006

Integral

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Please show us that you have put some effort into this porblem.

Aug 13, 2006

c00ky

Ok, i got this far:

http://putfile.com/pic.php?pic=main/8/22414282061.jpg&s=f10

This (i hope) is the 4 terms, i do not know what to do after this.

Last edited by a moderator: Apr 22, 2017

1. What is the general term for an expansion?

The general term for an expansion is "series". A series is a sequence of terms that are added together to form a sum.

2. What is the difference between a finite and an infinite expansion?

A finite expansion has a limited number of terms, while an infinite expansion has an unlimited number of terms. In other words, a finite expansion has an ending point, while an infinite expansion does not.

3. How is a series represented mathematically?

A series is represented using sigma notation, which is written as Σ. The variable below the sigma represents the starting term, while the variable above the sigma represents the ending term. The expression to the right of the sigma represents the terms being added together.

4. What is a geometric expansion?

A geometric expansion is a series where each term is found by multiplying the previous term by a constant number, called the common ratio. This type of expansion can either be finite or infinite, and the common ratio must be consistent throughout the series.

5. How do you find the sum of a series?

The sum of a series can be found by using a specific formula, depending on the type of series. For example, a finite arithmetic series can be found by using the formula Sn = n/2(a1 + an), where n is the number of terms, a1 is the first term, and an is the last term. For infinite series, the sum can be found by taking the limit of the series as it approaches infinity.