Use math induction to prove an expanded integral.

In summary, the conversation is about a student struggling with math induction in their intro to real analysis class. They are given a question to prove and are trying to figure it out on their own. Another user suggests starting with integrating by parts and using the induction hypothesis to prove it for n+1. The student eventually understands and asks about closing the thread.
  • #1
pzzldstudent
44
0
I am in intro to real analysis I, and we're on math induction now.

I did okay with math induction when I took discrete math, but it's more complex now.

Here is what we have to prove:

http://answerboard.cramster.com/advanced-math-topic-5-317406-0.aspx"

I'm quite lost. I will try to do as much as I can and see how far I get on my own.

Thank you.
 
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  • #2
Just start by integrating by parts. First see what happenes when n=1. Use integration by parts, and see whether you get the same thing as on the RHS. After that suppose that the equation holds for n, and prove that it holds also for n+1, by integrating again by parts, and using your induction hypothesis.
 
  • #3
I think I got it now. Thanks!

(How can I close this thread now that the question's been resolved?)
 
  • #4
i don't know ,but just leave it like this...it won't be a problem.
 
  • #5
thanks

ok, thanks.
 

1. What is mathematical induction?

Mathematical induction is a method of mathematical proof used to prove statements about integers or other discrete structures. It involves proving that a statement holds for the first value, and then showing that if it holds for any given value, it also holds for the next value.

2. How is mathematical induction used to prove an expanded integral?

In order to prove an expanded integral using mathematical induction, we first need to show that the statement is true for the first value, typically 0 or 1. Then, we assume that the statement holds for an arbitrary value, and use this assumption to prove that it also holds for the next value. This process is repeated until we have shown that the statement holds for all values, and therefore, the expanded integral is proven.

3. What are the steps to use mathematical induction for proving an expanded integral?

The steps for using mathematical induction to prove an expanded integral are as follows:

  1. Prove the statement for the first value.
  2. Assume the statement is true for an arbitrary value, typically denoted as k.
  3. Use this assumption to prove that the statement is also true for the next value, k+1.
  4. Repeat this process until the statement has been proven for all values.
  5. Conclude that the expanded integral is true.

4. Can mathematical induction be used for all types of expanded integrals?

Yes, mathematical induction can be used to prove all types of expanded integrals. As long as the statement can be proven for the first value, and assuming the statement is true for an arbitrary value allows us to prove it for the next value, mathematical induction can be applied.

5. Are there any common mistakes to avoid when using mathematical induction to prove an expanded integral?

One common mistake to avoid when using mathematical induction is assuming that the statement holds for all values without actually proving it for each value. It is important to go through each step of the induction process and show that the statement holds for every value, rather than just assuming it does. Additionally, it is important to make sure the statement is true for the first value, as this is the basis for the entire proof.

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