Write the 1st 6 terms of the power series for, along with the general power series using summation notation.

$\displaystyle y = e^{x}$

$\displaystyle y = e^{-x}$

$\displaystyle y = e^{-x^3}$

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$\displaystyle y = e^{x} \implies 1 + x + x^2/2! + x^3/3! + x^4/4! + x^5/5! + \cdots + \sum_{n=0}^{\infty} \frac{x^n}{n!}$

And then the next I am assuming is the same as above but alternating signs?

No idea for the 3rd.