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**[SOLVED] power series expansion for Laplace transform**

We are to find the Taylor series about 0 of e^t, take the tranform of each term and sum if possible. So I know the expansion of e^t is 1+x/1!+x^2/2!...... x^n/n! then taking the tranform, 1/s + (1/1!)(1!/s^2) +(1/2!)(2!/s3)..... and so on then the factorials cancel and I have in summation notation sum(1,inf.)1/s^n. I can see that. But answer says that equals 1/(s-1) and I am not seeing that.