How to Simplify a Series with Basic Algebra?

Thread starter kuahji
Start date Apr 20, 2008
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Algebra Basic algebra

In summary, a sum/series in basic algebra is a mathematical expression representing the addition of multiple terms, with a starting and ending term and each term denoted as an. To find the sum, one can use the formula Sn = (n/2)(a1 + ak) or Sn = (n/2)(2a1 + (n-1)d). The difference between an arithmetic and geometric series is that in an arithmetic series, the difference between each term is constant, while in a geometric series, the ratio between each term is constant. The nth term in a series can be found using different formulas depending on whether the series is arithmetic or geometric. Sums/series have many applications in real life, including in financial calculations

Apr 20, 2008

kuahji

[tex]\sum[/tex] (2^(2n)-(-7)^n)/(11^n)

The book has that expression equal to
[tex]\sum[/tex] (4/11)^n - [tex]\sum[/tex] (-7/11)^n

I'm not seeing how the first part changes to (4/11)^n. Wouldn't it be (2^2+2^n) & not 4^n? Or is there something else I'm missing?

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Apr 20, 2008

nicksauce

Science Advisor

Homework Helper

Fact:
[tex](x^y)^z = x^{yz}[/tex].
Does that help you out?

Apr 20, 2008

kuahji

Crude, nm. 2am & math doesn't mix sometimes. ^_^

1. What is a sum/series in basic algebra?

A sum/series in basic algebra is a mathematical expression that represents the addition of multiple terms. It can be written in the form of ∑n=1k an, where n is the starting term, k is the ending term, and an is the nth term in the series.

2. How do you find the sum of a series in basic algebra?

To find the sum of a series in basic algebra, you can use the formula Sn = (n/2)(a1 + ak), where n is the number of terms in the series, a1 is the first term, and ak is the last term. Alternatively, you can also use the formula Sn = (n/2)(2a1 + (n-1)d), where d is the common difference between each term.

3. What is the difference between an arithmetic and geometric series in basic algebra?

An arithmetic series in basic algebra is a series where each term is obtained by adding a constant value to the previous term. On the other hand, a geometric series is a series where each term is obtained by multiplying the previous term by a constant value. In an arithmetic series, the difference between each term is constant, while in a geometric series, the ratio between each term is constant.

4. How do you solve for the nth term in a series in basic algebra?

The nth term in a series in basic algebra can be found using the formula an = a1 + (n-1)d for an arithmetic series, and an = a1(r)^n-1 for a geometric series, where a1 is the first term, d is the common difference or ratio, and n is the term number. You can also use the general formula an = a1 + (n-1)c, where c is the coefficient of n in the series.

5. How can sums/series be applied in real life situations?

Sums/series have many applications in real life situations, such as calculating the total cost of items in a shopping list, determining the total distance traveled in a trip with different stopping points, or calculating the total number of bacteria in a population after a certain number of generations. They are also used in financial calculations, physics, and computer science, among others.