What is the solution to this puzzling brain teaser?

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Discussion Overview

The discussion revolves around a brain teaser involving a standard Normal probability distribution and its power series expansion. Participants are exploring how to approach the problem, particularly focusing on differentiation and series representation.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant expresses difficulty in approaching the problem and seeks assistance.
  • Another participant suggests that the problem involves differentiating the power series term by term to show it is an anti-derivative of the Normal distribution function.
  • A different participant questions how many terms should be differentiated, noting that their calculus teacher was also puzzled by the problem.
  • Another reply proposes finding the series representation of the antiderivative and summing it to identify a correspondence with the two expansions.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the approach to the problem, with some suggesting differentiation and others focusing on series representation. The discussion remains unresolved regarding the best method to tackle the brain teaser.

Contextual Notes

There are limitations regarding the assumptions made about the series and the number of terms to differentiate, which are not fully clarified in the discussion.

jmckennon
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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
 

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

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