Are we supposed to guess that f(x) is that sum?

That is not what I get. How did you get that?i got the interval of convergence for f(x) but not sure its right. -9<x<11

No, the sum is not equal to that! Perhaps you meant that the ratio test reduces to that- but that is not true either. How did you get (1/5)(x-1)< 1?for f'(x) i have

E (-1)^n+1 n(x-1)^n-1 / 5n

which equals (1/5)(x-1)<1

which equals -6<x<6

Pretty much nothing is correct here but since you don't show how you got these, I can't see how to correct it.well im not sure im doing this right so yeah any help?