Simplification of an equation, please help

[jackiepollock]

Hello! For the following series, I am trying to understand the last line( the one underlined with blue). How exactly does the series get simplified into the underlined equation? I thought it should be (-(r-1))!(1)^-r after plugging 0 in.

Thank you!

 

[Dr.Peterson]

I thought it should be (-(r-1))!(1)^-r after plugging 0 in.

Can you show how you got that? And how are you taking the factorial of a negative number?

 

[Steven G]

Please compute some more derivatives at x=0 and then try to determine f^(r)(0)