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Let f(x)=(x+1)ln(x+1).
Show that f′′(x)=x+11.
Let f(n) denote the nth derivative of f.
Using induction, prove that f(n)(x)=(x+1)n−1(−1)n(n−2)! for all n∈Z, n≥2.
Hence find the Maclaurin series expansion for f(x) as far as the term in x6.
Using your answer to part (c), find a decimal approximation for ln4.
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