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Question #a8879

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Apr 6, 2017

A formula to memorize is the MacLaurin series of #ln(1+x)#.

#ln(1+x)=sum_(n=0)^(oo)frac{(-1)^n(x)^(n+1)}{n+1}#

Therefore:
#ln(1+4x)=sum_(n=0)^oofrac{(-1)^n(4x)^(n+1)}{n+1}#

#=sum_(n=0)^oofrac{(-1)^n(4)^(n+1)(x)^(n+1)}{n+1}#

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