# Homework Help: Inverse laplace and power series

1. Sep 22, 2009

### oddiseas

1. The problem statement, all variables and given/known data

I am trying to figure out how to represent an inverse laplace transform by a power series. There is an example in my book but it is not very well explained.

f(s)=1/s+1 which i know is the transform of y=e^-t.

In the book they use the fact that L(t^n)= n!/s^n+1. and therefore a taylor series representation given by t^n/n!=the inverse of 1/s^n+1. Therefore our power series in s has this form. After this point i am totally lost. They state that 1/s+1 =1/s(1+1/s).
and the solution is therfore (1/s)-(1/s^2)+(1/s^3) etc.

Now id like to know, WHY do they take the factor of s out of the equation?
ANd then how do they find the coefficients of the s terms? do they differentite f(s) to find the coefficient of each s term? like we do for a taolr series
Is there an easier way?
and waht value of s, is it evaluated at to find the coefficients?
If someone understands this i would appreciate an explanation, because this book seems to always assume that the reader is a 20 year mathematics veteran or something!