This is a homework question and I am not really sure where to go with it. I have a lot of trouble with sequences and series, can I get a tip or push in the right direction?
Prove that $(1 - \frac{1}{n})^{-n}$ converges to $e$
17
$\begingroup$
sequences-and-series
-
0Could you define $e'$? – 2011-11-14
-
0I believe it is defined int his homework as just $e$, I will change the OP. – 2011-11-14
-
0use $\lim_{n \to \infty} (1+\frac{1}{n})^{n}=e$ – 2011-11-14
-
0@pedja: I think you need the stronger $\lim_{n \rightarrow \infty} (1 + \frac{x}{n})^n = e^x$. (Applied with $x = -1$.) – 2011-11-14
-
0Assuming you are to establish the limit, L' Hospital rule may be a good choice. – 2011-11-14
-
0@Robjohn: I wonder if your comment is confusing in the current state of the post :) (since the accepted answer has been changed) – 2012-03-07
-
0@Ilya: deleted more like. I guess that my comment should have been to that answer. We should leapfrog deletes :-) – 2012-03-07