Geometric power series of f(x)=6/(2-x) c=1

In summary, a geometric power series is an infinite series where each term is a constant multiple of the previous term. The series for f(x)=6/(2-x) c=1 can be calculated by first finding the value of c, which is given as 1, and then finding the value of x that makes the series convergent. The significance of c=1 in the series for f(x)=6/(2-x) is that it indicates the first term in the series is 1. Geometric power series have various real-life applications, such as calculating compound interest and modeling population growth. The limit of the geometric power series for f(x)=6/(2-x) c=1 is infinity, but the series only converges
  • #1
NIZBIT
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Find the geometric power series for the given function:

f(x)=6/(2-x) c=1

I am stumped on this one. I've tried for an hour on this one with no luck. Could someone help?
 
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  • #2
Write it as [tex] 6\left(\frac{1}{2-x}\right) [/tex]. You have to get rid of the 2 so write it as follows:

[tex] 6\left(\frac{1}{2(1-\frac{x}{2})}\right) \rightarrow 3\left(\frac{1}{1-\frac{x}{2}}\right) [/tex]
 
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Related to Geometric power series of f(x)=6/(2-x) c=1

1. What is a geometric power series?

A geometric power series is a type of infinite series where each term is a constant multiple of the previous term. It can be written in the form of f(x) = c + cx + cx^2 + cx^3 + ..., where c is a constant and x is the variable.

2. How is the series for f(x)=6/(2-x) c=1 calculated?

The series for f(x)=6/(2-x) c=1 can be calculated by first finding the value of c, which is given as 1. Then, we need to find the value of x that makes the series convergent, which in this case is x=2. Finally, we plug in these values into the formula for a geometric power series and simplify the expression to get the series for f(x)=6/(2-x) c=1.

3. What is the significance of c=1 in the series for f(x)=6/(2-x)?

The value of c=1 in the series for f(x)=6/(2-x) indicates that the first term in the series is 1. This means that the series starts with 1 and each subsequent term is a multiple of the previous term.

4. How can geometric power series be used in real-life applications?

Geometric power series have many applications in various fields such as finance, physics, and engineering. For example, they can be used to calculate compound interest, model population growth, and approximate solutions to differential equations.

5. What is the limit of the geometric power series for f(x)=6/(2-x) c=1?

The limit of the geometric power series for f(x)=6/(2-x) c=1 is infinity. This means that as x approaches 2, the terms in the series become larger and larger, resulting in an infinite sum. However, the series only converges for values of x less than 2, as the series will diverge for x=2.

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