- #1
jmher0403
- 22
- 0
Homework Statement
Taylor series of f(x)=ln(x+1) centred at 2
Homework Equations
from 0 to infinity ∑ cn(x-a)n
cn = f(n)(a)/n!
The Attempt at a Solution
f(x) = ln(1+x)
f'(x) = 1/(1+x)
f''(x) = -1/(1+x)2
f'''(x) = 2/(1+x)3
f''''(x) = -6/(1+x)4f(2) = ln(3) = 1.0986
f'(2) = 1/3
f''(2) = -1/9
f'''(2) = 2/27
f''''(2) = -6/81
f(2)+f'(2)(x-2)+f''(2)(x-2)2/2!+f'''(2)(x-2)3/3!+f''''(2)(x-2)4/4!
I can't see any pattern except partially ..(-1)n-1(x-2)n/3nn!
I have no idea what to do with ln3
Please help!