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Math Help - Simplifying a summation

  1. #1
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    Simplifying a summation

    Hi, how would you simplify this summation. I have the steps, but I don't see it. Can someone explain it? =]

    Sum from n = 0 to infinity: [(lambda*e^t)^n]/n!
    The next step is: e^(lambda*e^t)

    Thanks!
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by feiyingx View Post
    Hi, how would you simplify this summation. I have the steps, but I don't see it. Can someone explain it? =]

    Sum from n = 0 to infinity: [(lambda*e^t)^n]/n!
    The next step is: e^(lambda*e^t)

    Thanks!
    okay, so this step is just working backwards. you have to know the formula for the taylor expansion of e. it goes like this:



    so you notice in your question, what is in place of x is lambda*e^t, so you just replace x with that in the above formula, so you see on the left it is equal to e^(lambda*e^t)
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    wow! Thanks! xD
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