Ok, so I've got the following problem:
Find an expression for the following McLaurin-series:
Σ (((n^2) - n +1) / n!) * x^n
(from n = 0 to infinity).
I decided to start with the known McLaurin series for e^x:
e^x = Σ (x^n) / n!
I then differentiate and get:
e^x = Σ (n*(x^(n-1))) / n!
I differentiate one more time and get:
e^x = Σ (((n^2) - n) / n!) * x^(n-2)
I can't get any further than this though. So what I need now is to get the (+1) in the numerator of the n-term, and x^(n-2) has to be reversed back to x^n. Can I multiply e^x with x^2 to get the x taken care of? And how do I get the (+1) term?
Any tips would be greatly appreciated!