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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- Mar 5th 2007, 07:42 AMfeiyingxSimplifying 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! - Mar 5th 2007, 07:59 AMJhevon
okay, so this step is just working backwards. you have to know the formula for the taylor expansion of e. it goes like this:

http://upload.wikimedia.org/math/e/c...0506dc83ae.png

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) - Mar 5th 2007, 08:22 AMfeiyingx
wow! Thanks! xD