How do you find the maclaurin series expansion of #ln(1+x)#?

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Answer 1 · 2015-10-11T03:37:52

See the explanation.

#f(x) = ln(1+x)#

#f'(x) = 1/(1+x) = (1+x)^-1#

#f''(x) =-(1+x)^-2#

#f'"'(x) =2(1+x)^-3#

#f^((4))(x) =-6(1+x)^-4#

#f^((5))(x) =30(1+x)^-5#

#f^((n))(x) =(-1)^(n-1) (n-1)! (1+x)^-n#

Now use the formula for a Maclaurin Series.

Note
#f^((n))(0) =(-1)^(n-1) (n-1)!#