# Determine the Maclaurin series representation for f(x)=e^x/x ?

Jun 1, 2018

The maclaurin series for ${e}^{x}$ is

f(x) = 1 + x + x^2/2 + x^3/(3!) + x^4/(4!) + ...

The maclaurin series for ${e}^{x} / x$ is therefore

f(x) = 1/x + x/x + x^2/(2x) + x^3/(3! * x) + x^4/(x * 4!)

f(x) = 1/x + 1 + x/2 + x^2/(3!) + x^3/(4!)

The general term is

f(x) = sum_(n= 0)^oo x^(n-1)/(n!)

Hopefully this helps!