What is the solution to this puzzling brain teaser?

[jmckennon]

I have been looking at this problem for quite some time and have been unable to figure out how to approach it.

the problem is in the attachment. It's from a brain teaser that my teacher gave us in class and it's so puzzling that I need to know how to do it. Any help would be EXTREMELY appreciated

 

[HallsofIvy]

What you have is the standard Normal probability distribution and a power series expansion for it. You want to show that the series is, in fact, an anti-derivative of the given function. To do that, differentiate the series term by term.

 

[jmckennon]

How many terms should i differentiate the series too? I brought the problem to my calculus 3 teacher and she was puzzled by it as well.

 

[HeisenBerg46]

Find the series representation of the antiderivative and sum it out until you see a correspondence in the two expansions.