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

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Answer 1 · 2018-06-01T05:05:55

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!