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Math Help - summation problem

  1. #1
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    summation problem

    If I am reducing the lower limit of a summation how does this work algebraically

    I have this as a solution and don't know where it comes from

    Summation from x=1 to infinity of (1/2*exp(t))^x

    The lower limit is then reduced;

    1/2*exp(t) * Summation from x=0 to infinity of (1/2*exp(t))^x

    Where does the 1/2*exp(t) come from ??

    I thought it was x=0 for f(x) added to the expression but that is simply 1
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  2. #2
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    Quote Originally Posted by revolution2000 View Post
    If I am reducing the lower limit of a summation how does this work algebraically

    I have this as a solution and don't know where it comes from

    Summation from x=1 to infinity of (1/2*exp(t))^x

    The lower limit is then reduced;

    1/2*exp(t) * Summation from x=0 to infinity of (1/2*exp(t))^x

    Where does the 1/2*exp(t) come from ??

    I thought it was x=0 for f(x) added to the expression but that is simply 1
    In general \sum_{n=1}^N f(n) = \sum_{n=0}^{N-1}f(n+1) so in your case the generator becomes \left(\frac{1}{2}e^t\right)^{x+1}or \frac{1}{2}e^t \left(\frac{1}{2}e^t\right)^{x}
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