Question

How do I find the first three non zero terms of the MacLaurin series expansion of y = e^(x-1) / x

Answer 1

you know that the series for e^x is ∑x^k/k!

so the series for e^(x-1)/x = 1/(ex) ∑x^k/k!
= 1/e (1/x + 1/1! + x/2! + x^2/3! + ...)
note that this does not converge for x=0