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Thread: Riemann integrable...

  1. #1
    Super Member maxpancho's Avatar
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    Riemann integrable...

    Cannot understand how the last two equalities are obtained. Could someone help?
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    Re: Riemann integrable...

    Quote Originally Posted by maxpancho View Post
    Cannot understand how the last two equalities are obtained. Could someone help?
    Note that $\Large\sum\limits_{k = 1}^N {f(k)} - \sum\limits_{k = 1}^N {f(k - 1)} = f(N) - f(0)$. If that is not clear then write out the sum with $N=5$. If it is still not clear, see your tutor.

    Finally, $\large x_N=a~\&~x_0=b$
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    Super Member maxpancho's Avatar
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    Re: Riemann integrable...

    Oh okay. So we offset the two sums by one step and hence get the last and first one. I was thinking about direct transformation of the sums into their corresponding terms, hence couldn't understand what happened.
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