The limit, asnapproaches infinity, of (1 + (1/n))^n=e(bye, I mean 2.71828). Use this to find the limit of the following sequence:

sn= ((n+2)/(n+1))^(n+3)

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- Apr 5th 2009, 11:54 AMbearej50limit and sequence
The limit, as

*n*approaches infinity, of (1 + (1/*n*))^*n*=*e*(by*e*, I mean 2.71828). Use this to find the limit of the following sequence:

s*n*= ((*n*+2)/(*n*+1))^(*n*+3) - Apr 5th 2009, 11:59 AMChris L T521
$\displaystyle \begin{aligned}\lim \left(\frac{n+2}{n+1}\right)^{n+3}&= \lim\left(\frac{n+1+1}{n+1}\right)^{n+3}\\ &= \lim\left(1+\frac{1}{n+1}\right)^{n+3}\\&=\lim\lef t(1+\frac{1}{n+1}\right)^{\left(n+1\right)\left(\f rac{n+3}{n+1}\right)}\\ &= e^{\lim\frac{n+3}{n+1}}\\&=\boxed{e}\end{aligned}$

- Apr 5th 2009, 12:00 PMJhevon