Question

Please Help: Find the radius of convergence of f(x)=6ln(7-x) as a MacLaurin series (around x=0)

Answer 1

Taken the first 4 derivatives but can't find a pattern

Answer 2

f(0)=6ln(7)
f'(0)=-6(7)^(-1)
f''(0)=-6(7)^(-2)
f'''(0)=-12(7)^(-3)
f(4)(0)=-36(7)^(-4)

Answer 3

This is above my current level but I think the is something like: f^n = n*(the previous constant): So f^1 is just -6, f^2 is still just -6 since the pattern one step behind. f^3=-6*2=12, f^4= -12*3=-36 it works at least up to f^6 which is -720(7)^-6: the pattern: f^5= -36*4= -144, f^6= -144*5=-720