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ptolema
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Homework Statement
find Taylor polynomial for ln x of degree n, at 2
(Pn,2(x))
Homework Equations
Pn,1(x)= (x-1) - (x-1)2/2 + ... + (-1)n-1(x-1)n/n
The Attempt at a Solution
there doesn't seem to be an obvious pattern to this. the coefficients for n=1 to n=4 are 2, -8, 24, -64. there is a common factor of 2, yes, but this doesn't account for the sign changes. the first term is ln 2, a positive number, then the next is (x-2)/2, another positive coefficient. how can i find the formula expressed with n and x for each term?