Power Series Problem: Determine Interval of Convergence

In summary, the conversation discusses determining the series of a given function and finding the sum of the first four nonzero terms. It also mentions the need to check the interval of convergence. The original function is not specified.
  • #1
arl146
343
1
a) Determine the series of the given function. In the first box after the summation symbol, type in -1 or 1 indicating whether the series is alternating or not.
b) Write out the sum of the first four nonzero terms of the series representing this function.
c) Determine the interval of convergence. The outside boxes require the endpoints and the inside boxes require the symbol < or <=.

I already got a.) which is sum from n=0 to infinity [ (-1)^n *(x/sqrt(6))^(2n+1) ] / (2n+1)
I think I got b.) not too sure if this one is right but i got (x/sqrt(6))-(x^3/(3*6^(3/2)))+(x^5/(5*6^(5/2)))-(x^7/(7*6^(7/2))).
And so I just need someone to check b for me and I don't even know what to do for the interval of convergence.
 
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  • #2
Determine the series of the given function.
What's the original function?
 

Related to Power Series Problem: Determine Interval of Convergence

1. What is a power series?

A power series is an infinite sum of terms, where each term is a constant multiplied by a variable raised to some power. It is often used in mathematics to approximate functions.

2. How do you determine the interval of convergence for a power series?

To determine the interval of convergence, you must use the ratio test or the root test. These tests involve taking the limit of the absolute value of the ratio or root of consecutive terms in the series. If the limit is less than 1, the series converges. Otherwise, it diverges.

3. What is the significance of the interval of convergence?

The interval of convergence represents the range of values for the variable in the power series that will result in a convergent series. It is important for determining the accuracy and usefulness of the power series in approximating a function.

4. Can a power series have an infinite interval of convergence?

Yes, a power series can have an infinite interval of convergence. This means that the series will converge for all values of the variable. This is typically the case for power series with a variable raised to a negative power.

5. How can the interval of convergence be used to approximate a function?

By evaluating the power series at a specific value within the interval of convergence, the resulting sum can be used to approximate the value of the function at that point. The more terms included in the power series, the more accurate the approximation will be.

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