Question

How would one write a Maclaurin series for (x^2)e^(x^2)) in sigma notation?

Answer 1

I understand the basic format, I just don't know how to deal with the \[f ^{k}(0)\] portion.

Answer 2

It's surprisingly easy once you know the trick, which should come as a good relief to you.

Do you know the Maclauren series for \(e^x\)?

Answer 3

\[\sum_{n=0}^{\infty}x ^{k}/k!\] ?

Answer 4

yes

Answer 5

replace \(x\) by \(x^2\) to get \(e^{x^2}\)

Answer 6

But am I supposed to substitute 0 into f(x) and just insert that into the summation?

Answer 7

you wrote \[e^x=\sum_{n=0}^{\infty}x ^{k}/k!\] right?

Answer 8

yes

Answer 9

so \[e^{x^2}=\sum_{n=0}^{\infty}(x^2) ^{k}/k!\]

Answer 10

which you can clean up easily