Thread: 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!

Originally Posted by feiyingx

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)

wow! Thanks! xD