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Math Help - Does anyone have general strategies for converting a Riemann sum to a integral?

  1. #1
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    Does anyone have general strategies for converting a Riemann sum to a integral?

    I need to deal some of question of this type recent,but I always get stuck.
    ex.
    \sum_{m=k}^{(tk^2)/2}\frac{1}{\sqrt{(\pi\frac{tk^2}{2})}}*exp{\frac{-m^2}{2tk^2}}
    tons of thanks in advance,if anyone has ideas

    my teacher said it approximately equals to \sqrt{\frac{2}{\pi}}\int_{\frac{1}{\sqrt{t}}}^{inf  inity} e^{-x^{2}}\,dx

    but I have no idea how to convert it.
    Last edited by kimkim007; April 1st 2013 at 12:42 PM.
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  2. #2
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    Re: Does anyone have general strategies for converting a Riemann sum to a integral?

    Quote Originally Posted by kimkim007 View Post
    I need to deal some of question of this type recent,but I always get stuck.
    ex.
    \sum_{k=0}^{(tk^2)/2}((1/sqrt{(pi*(tk^2)/2)}*exp{-(m^2)/(2tk^2)}
    tons of thanks in advance,if anyone has ideas
    A "Riemann sum" is always of the form \sum_{k=0}^N f(x_k)\Delta_k and the reduces to the integral \int_{f(x_0)}^{f(x_N)} f(x)dx.
    Basically, what you need to do is determine which part of the sum you want to be " f(x_k)" and which part you want to be " \delta_k".

    However, you " tk^2/2" as the upper limit as your sum. That is impossible. You cannot have "k", the sum index in the upper limit.
    Thanks from kimkim007
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  3. #3
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    Re: Does anyone have general strategies for converting a Riemann sum to a integral?

    Thank for you reply Hallsoivy,I am new to latex,there is a typo in my original formula.
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  4. #4
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    Re: Does anyone have general strategies for converting a Riemann sum to a integral?

    HallsofIvy,I amend my thread. could you plz look at it again. I don't know how to convert one to other one.
    Last edited by kimkim007; April 1st 2013 at 12:38 PM.
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