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Defintion of e as a limit

  • Thread starter blerg
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Homework Statement


Show that [tex] x_n = \left(1 + \frac{1}{n}\right)^{n+1}[/tex] is decreasing and bounded below


Homework Equations





The Attempt at a Solution


I have tried all sorts of things and none some to be working. I tried expanding it using the binomial theorem, but there are more terms in [tex] x_{n+1} [/tex] than [tex] x_n [/tex] so i didn't see an easy way to compare them. I tried looking at [tex] \frac{x_{n+1}}{x_n} [/tex] and [tex] x_nx_{n+1} [/tex] with nothings giving me and progress. Any suggestions?
 

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