find the maclaurin series of e^(3x) + e(-3x)
The Attempt at a Solution
I'm not sure about finding taylor and maclaurin series, I understand perfectly how to find the terms of the series...But how do I put it into a general term do I just have to recognize the pattern by looking at it? anyway...
to attempt this problem I was thinking you use the known maclaurin series for e^x which has a general term of x^n / n! it will be (3x)^n / n! for the first term and (-3x)^n / n! for the 2nd term I'm unsure of combining these The answer is 2*3^2n*x^2n/(2n)! What I do not understand is how they got (2n)! I thought it should be 2(n!) and also I thought there should be a negative in the numerator...can anyone explain to me these parts I do not understand...my textbook has one small paragraph on these series and it does not explain much...