Question
Find the first three nonzero terms and the general term of the Maclaurin series generated by e^(-6x).
My answer: 1 + x + (x^2)/2, general term (x^(n-1))/(n-1)!
My answer: 1 + x + (x^2)/2, general term (x^(n-1))/(n-1)!
Answers
Reiny
the expansion is
e^x = 1 + x/1! + x^2/2! + x^3/3! + .... + e^(n-1)x)/(n-1)! + ....
you just stated the first 3 terms and the general term of the general series.
e^(-6x) = 1 + (-6x) + (36x^2)/2 + (-216x^3)/6 + ....
= 1 - 6x + 18x^2 - 36x^3 + ....
general term : e^(n-1)(-6x)/(n-1)!
e^x = 1 + x/1! + x^2/2! + x^3/3! + .... + e^(n-1)x)/(n-1)! + ....
you just stated the first 3 terms and the general term of the general series.
e^(-6x) = 1 + (-6x) + (36x^2)/2 + (-216x^3)/6 + ....
= 1 - 6x + 18x^2 - 36x^3 + ....
general term : e^(n-1)(-6x)/(n-1)!