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How do you find the power series representation for the function #f(x)=(1+x)/(1-x)# ?

1 Answer

Sep 9, 2014

Recall:
#1/{1-x}=sum_{n=0}^infty x^n=1+sum_{n=1}^infty x^n#
By multiplying by #x#,
#x/{1-x}=sum_{n=0}^infty x^{n+1}=sum_{n=1}^infty x^n#

So,
#{1+x}/{1-x}=1/{1-x}+x/{1-x}=1+sum_{n=1}^infty x^n+sum_{n=1}^infty x^n#
#=1+2sum_{n=1}^infty x^n#

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