i've gotten part of the way through into this problem and i'm just a little bit confused..
find the maclaurin series of f(x)= xe^x
and i can't solve it with a geometric series, i have to use the definition for a maclaurin series itself
so, i took the 1st, 2nd, & 3rd derivatives, and determined that the pattern was that the nth derivative will be e^x(n+x)
then i said that evaluated at zero, the nth derivative is e^0 (n+0) = n
so i plugged it into the formula of the nth derivative evaluated at zero times x^n all over n!
i said the first few terms were x + x^2 + 1/2 x^3 + 6x^4+...
now i'm sort of clueless as to where to go from here