What is the Maclaurin series for f of x equals x squared times e to the power of x to the power of 2?

Question

What is the Maclaurin series for ?

A
B
C
D

Answer 1

It is D.

The Maclaurin series for e^x is ∑x^n/n!

Thus, the Maclaurin series for e^(x^2) is replacing x with x^2, ∑(x^2)^n/n! = ∑x^2n/n!

and the Maclaurin series for x^2e^(x^2) is ∑x^2x^2n/n! = ∑x^(2n+2)/n!