- #1
kde2520
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Homework Statement
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.
Homework 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.
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.