Power series

[juztbenja]

A function f take value -9 from x = 0. The n'th derivative is given by



f is analytical. on the interval (-3,3). What is f(5/2)

So I've tried to use the formula for Maclaurin series so that I get: (4/3^n) * x^n. And then get the sum = 12/(3-x) and try to put in 5/2 for x, then get 24. But I don't get the answer I'm looking for. I also tried to do this f(5/2) = -9 + 24 = 15 which is also the wrong answer... What am I doing wrong? Feel kinda stupid right now XD

 

[blamocur]

To get [imath]\frac{12}{3-x}[/imath] you need to start your series from [imath]n=0[/imath], but you are starting from [imath]n=1[/imath].