Power Series for e^x Homework Help

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The discussion centers on finding the correct value of b in the power series for e^x, specifically for the function (1/1+b). The user initially calculates the answer as ln(-5/6) but is informed that the correct answer is ln(5/6). The confusion arises from the user's calculations, which may involve misinterpretation of the series or limits. Other participants suggest reviewing the work for proper notation and limits to identify the error. The conversation emphasizes the importance of careful mathematical notation in solving power series problems.
islandboy401
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Homework Statement



Problem: Find the value of b for which
21.JPG



Homework Equations



Power series for (1/1+x) or in this case, power series for (1/1+b)

The Attempt at a Solution




I keep getting ln (-5/6) as the answer, but apparently the correct answer is ln (5/6). I do not see why.

Please look at my work and tell me what I am doing wrong.

21w.jpg
 
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I can't see the problem.
 
Go back and write it out with the sums, limits, and ns in their proper places and I think you will see your error.
 

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