Power Series from MTW 19.1: Explained?

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zn5252
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hello
Please see attachment which is a snapshot from MTW first page of chapter 19. Can someone please elaborate on how the equations 19.3b and c can be explained ?
I know that equation 19.3a is a familiar formula but not so much the other two. I'm just confused.
Thank you,
Long live & clear skies.
 

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