Coefficients in a quotient of sums

• I
• Sturk200
In summary, the conversation discusses how to find the coefficient of the order $x^j$ term in a quotient of two infinite power series. The suggested approach is to use division, similar to dividing polynomials, and there is an example provided on page 3 of a resource. The process may be tedious, but it is effective.
Sturk200
Is there a general way to express, for instance, the coefficient of the order $x^j$ term in the expression

$$\frac{\Sigma_{n}^{\infty}a_nx^n}{\Sigma_{m}^{\infty}b_mx^m}$$ ?

Basically I am working with a quotient of two infinite power series and I want to know the term in this quotient that is proportional to a particular power of the expansion variable. Am I even guaranteed that there will be such a term? How do I find it?

Sturk200 said:
Is there a general way to express, for instance, the coefficient of the order $x^j$ term in the expression

$$\frac{\Sigma_{n}^{\infty}a_nx^n}{\Sigma_{m}^{\infty}b_mx^m}$$ ?

You could try doing division, similar to the way that one divides one polynomial by another polynomial. There's an example on page 3 of http://www2.fiu.edu/~aladrog/IntrodPowerSeries.pdf

Stephen Tashi said:
You could try doing division, similar to the way that one divides one polynomial by another polynomial. There's an example on page 3 of http://www2.fiu.edu/~aladrog/IntrodPowerSeries.pdf

That was a bit tedious, but I think it actually worked for my purpose. Thanks!

1. What are coefficients in a quotient of sums?

Coefficients in a quotient of sums refer to the numbers that are multiplied by the variables in a fraction that contains multiple terms in the numerator and denominator. They are used to simplify algebraic expressions.

2. How do you find the coefficients in a quotient of sums?

To find the coefficients in a quotient of sums, you can use the distributive property to multiply the numbers outside the parentheses by each term inside the parentheses. The resulting numbers are the coefficients.

3. Can coefficients be negative in a quotient of sums?

Yes, coefficients can be negative in a quotient of sums. This happens when there is a negative number outside the parentheses, or when a negative number is multiplied by a variable inside the parentheses.

4. What is the purpose of finding coefficients in a quotient of sums?

The purpose of finding coefficients in a quotient of sums is to simplify algebraic expressions and make them easier to work with. It also helps in solving equations and understanding the relationship between different variables.

5. Are coefficients important in math?

Yes, coefficients are important in math. They are used in various mathematical operations such as multiplication, division, and solving equations. They also help in understanding the behavior and relationships between variables in algebraic expressions.

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