(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

With n>1, show that (a) [tex]\frac{1}{n}[/tex]-ln[tex]\frac{n}{n-1}[/tex]<0

and (b) [tex]\frac{1}{n}[/tex]-ln[tex]\frac{n+1}{n}[/tex]>0

Use these inequalities to show that the Euler-Mascheron constant (eq. 5.28 - page330) is finite.

2. Relevant equations

This is in the chapter on infinite series, in the section on Taylor Expansion, so I guess Taylor, Maclaurin, and Binomial theorem are fair game.

3. The attempt at a solution

I first wrote the logarithm as a difference of logs and then tried to expand them in the Maclaurin series. But that apparently doesn't work since ln(0) and 1/0 are undefined...

I also don't understand the statement at the end. Is that supposed to be a hint or a third part to the problem?

Any help would be great, thanks.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Taylor expansion problem 5.6.9 in Math Methods for Physicists, 6th ed Arfken & Weber

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