e^[(x-1) - 1/2 (x-1)^2 + (x-1)^3 /3 -(x-1)^4 /4 + ....] is equal to?

1 Answer
Jun 17, 2017

The answer is =x

Explanation:

Let y=(x-1)

The exponent is

=y-y^2/2+y^3/3-y^4/4+................

This series is

ln(1+y)=y-y^2/2+y^3/3-y^4/4+................

Replace y by (x-1)

ln(1+y)=ln(1+x-1)=lnx

Therefore,

e^(ln(1+y))=e^lnx=x