Use math induction to prove an expanded integral.

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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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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.
 
I think I got it now. Thanks!

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

ok, thanks.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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