SOLUTION: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = ln(1 + 2x)

Algebra ->  Sequences-and-series -> SOLUTION: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = ln(1 + 2x)      Log On


   

Question 1185530: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that
Rn(x) → 0.]
f(x) = ln(1 + 2x)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
%22f%27%28x%29%22+=+2%2A%281%2B2x%29%5E%28-1%29
%22f%27%27%28x%29%22+=+%28-1%29%5E1%2A2%5E2%2A%281%2B2x%29%5E%28-2%29
%22f%27%27%27%28x%29%22+=+%28-1%29%5E2%2A2%5E3%2A2%21%2A%281%2B2x%29%5E%28-3%29
....
Inductively, , and so
f%5E%28%28k%29%29%280%29+=+%28-1%29%5E%28k-1%29%2A2%5Ek%2A%28k-1%29%21

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