Power Series Problem: Am I Correct?

In summary, the conversation discusses a disagreement with a part of a solution to a power series problem. The problem statement and a portion of the solution are provided, with a highlighted error in the solution. The individuals agree that the solution is incorrect and should instead include + a_n outside the right square bracket.
  • #1
temaire
279
0

Homework Statement


Well, I'm not getting any problems from the question, but there is a part of the solution that I don't agree with.

Here's the problem statement:
[PLAIN]http://img810.imageshack.us/img810/5387/powerseriesproblem.png

Here's part of the solution:
[PLAIN]http://img38.imageshack.us/img38/2104/powerseries.png


The Attempt at a Solution


As you can see, in the solution I circled +1 in red. I don't think it should be there. Instead, I think outside the right square bracket there should be [tex]+ a_n[/tex]

Am I correct?
 
Last edited by a moderator:
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  • #2
I agree with you. Looks like there's a mistake in the solutions.
 

1. What is a power series?

A power series is a mathematical series that involves raising a variable to a power and summing the resulting terms. It is typically used to approximate a function by breaking it down into simpler components.

2. How do I know if my solution to a power series problem is correct?

To determine if your solution is correct, you can use the ratio test or the root test to check for convergence. You can also plug your solution back into the original function and see if it produces the desired result.

3. What are some common mistakes when solving power series problems?

Some common mistakes include forgetting to include all terms in the expansion, using the wrong power in the terms, and not simplifying the solution fully. It is also important to check for convergence before assuming a solution is correct.

4. Can I use a calculator to solve power series problems?

While a calculator can be helpful for computing individual terms in a power series, it is generally recommended to solve the problem by hand using algebraic manipulation and power series formulas. This ensures a better understanding of the concept and helps avoid errors.

5. How can I improve my skills in solving power series problems?

To improve your skills, it is important to practice regularly and familiarize yourself with different types of power series problems. You can also seek help from a tutor or attend a workshop to learn new techniques and strategies for solving these problems.

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