P pamw New member Joined Jan 10, 2007 Messages 8 Mar 25, 2007 #1 help! \(\displaystyle \lim_{x \to \infty} \[ \left( {\frac{{n + 2}}{n}} \right)^n \left( {\frac{{n - 3}}{n}} \right)^n \]\) I don't know how to simplify this.
help! \(\displaystyle \lim_{x \to \infty} \[ \left( {\frac{{n + 2}}{n}} \right)^n \left( {\frac{{n - 3}}{n}} \right)^n \]\) I don't know how to simplify this.
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,203 Mar 26, 2007 #2 Take note that: \(\displaystyle \L\\\lim_{n\to\infty}\left(1+\frac{1}{n}\right)^{n}=e\) Therefore, \(\displaystyle \L\\\lim_{n\to\infty}\left(1+\frac{2}{n}\right)^{n}=e^{2}\) Can you finish?. See what's going on?.
Take note that: \(\displaystyle \L\\\lim_{n\to\infty}\left(1+\frac{1}{n}\right)^{n}=e\) Therefore, \(\displaystyle \L\\\lim_{n\to\infty}\left(1+\frac{2}{n}\right)^{n}=e^{2}\) Can you finish?. See what's going on?.
