IF y=x+x2/2+x3/3+x4/4+....... THEN PROVE THAT x=y-y2/2!+y3/3!+y4/4!+.......
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1 Answers
21here it should be mentioned that mod(x)<=1
then using series expansion of ln(1-x) we have
-ln(1-x) = x+x2/2+x3/3+x4/4+.......=y
hence,
ln(1-x)=-y
(1-x)=e^(-y)
x= 1-e^-y
using series expansion for e^-y we get the desired
result.
Shambo Mohanty THANK YOU K.K.A. IT IS THE RIGHT ANSWERUpvote·0· Reply ·2012-06-15 02:46:42