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Math Help - Summation

  1. #1
    Member helloying's Avatar
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    Summation

    It is given that U_1 =e^2 , U_{r+1} - U_r = (e-10)e^{r+1}

    By considering \sum^{n}_{r=1}(U_{r+1} - U_r , show that, U_n =e^{n+1}

    I dont know do the summation
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  2. #2
    MHF Contributor

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    You are told that U_{r+1}- U_r= (e- 10)e^{r+1}= e(e-10)e^r
    so \sum_{r=1}^n(U_{r+1}- U_r)= e(e-10)\sum_{r=1}^n e^r.

    \sum_{r=1}^n e^r= \sum_{r=0}^n e^r- 1
    That's a geometric series. Do you know the formula for the sum of a geometric series?
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