(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Taylor series of f(x)=ln(x+1) centred at 2

2. Relevant equations

from 0 to infinity ∑ cn(x-a)n

cn = f(n)(a)/n!

3. 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)4

f(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 cant see any pattern except partially ..(-1)^{n-1}(x-2)^{n}/3^{n}n!

I have no idea what to do with ln3

Please help!

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# Homework Help: Taylor series of f(x)=ln(x+1) centred at 2

**Physics Forums | Science Articles, Homework Help, Discussion**