Give the first three terms and the general term for ((e^x)-1)/x
The Attempt at a Solution[/B]
I wasn't sure if I would be able to take the e^x series and subtract 1 from each term and divide each term by x. I was also thinking of splitting it into e^x/x -1/x and adding both series, but I'm not sure how to calculate series for either of those. My textbook says the answer is 1+ x/2! + x^2/3! +...+ x^n/(n+1)! which I do not see how they got that answer. I'm pretty lost on this one, I'm new to series and trying to get a grasp on it so some help would be appreciated.
Some overall questions: what is series for 1/x? I would think you could say 1/(1-(1-x)) to use the series for 1/(1-x) but I don't see how you could get the answer in the book if this was true.
If I have a series for a function like f(x)/x can I just take a known series for f(x) and divide each term by x to get series for f(x)/x? I feel like you can but I'm new to this and not sure. Also same goes for f(x) -1, would you subtract 1 from each term?