Question

[Calculus] Taylor series given:
f(x) = ln(x) a=4
f(x) = ln(4) + sum(....)

Answer 1

so my first step was to try to find the nth derivative of f(4)
so f'(x) = 1/x f''(x)= -1/x^2 f'''(x) = 2/x^3 f4(x) = -6/x^4 and so on
....f'(4) = 1/41 f''(4)= -1/4^2 f'''(4) = 2/4^3 f^4(4)= -6/4^4 and so on
so i think fn(4) = (-1)^(n+1)/x^n * something
I can't figure out how to fix the numerator for fn(4)
I would then take Σ (fn(4)/n!) *(x-4)n to find the radius of convergence