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Math Help - How to write this function as an integral?

  1. #1
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    How to write this function as an integral?

    Prove that the following sequence converges, and find its limit.

    a_n=\frac{1}{n^3}\sum_{k=1}^nk^2cos(\frac{k\pi}{n}  )

    I'm stuck on just determining what function this is...
    I know b-a=1 and (I think) a=0 so the integral is from 0 to 1. Any other help on this?
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  2. #2
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    It's a Riemann sum for the function f(t)=t^2\cos(\pi t), can you see why?
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  3. #3
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    Quote Originally Posted by Krizalid View Post
    It's a Riemann sum for the function f(t)=t^2\cos(\pi t), can you see why?
    That's what I thought, I just wasn't sure. The sum is from 0 to 1, right?
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  4. #4
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    Yes.
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