Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do n
ot show that Rn(x) → 0.] f(x) = ln(1 + 2x)
1 answer:
Answer:

Step-by-step explanation:
The Maclaurin series of a function f(x) is the Taylor series of the function of the series around zero which is given by

We first compute the n-th derivative of
, note that

Now, if we compute the n-th derivative at 0 we get

and so the Maclaurin series for f(x)=ln(1+2x) is given by

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