How do you find the power series representation for the function #f(x)=ln(5-x)# ?

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Answer 1 · 2014-10-02T00:21:53

#f(x)=-sum_{n=1}^infty(x-4)^n/n#

Let us look at some details.

Since

#ln(1-x)=-sum_{n=1}^inftyx^n/n#,

by replacing #x# by #(x-4)#,

#ln(5-x)=ln[1-(x-4)]=-sum_{n=1}^infty(x-4)^n/n#.

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