Calculate limit of every sequence definite in N* by :
First sequence :
Second sequence :
$\displaystyle lim_{n\rightarrow \infty}\left(1+\frac{1}{n}\right)^{n}=\left(1+\fra c{1}{\infty}\right)^{\infty}$
you know that $\displaystyle \frac{1}{\infty}=0$
so the final thing will happen
$\displaystyle \left(1+0\right)^{\infty}=1$ there is a limit so it is converge
the second sequence is less than 2
my solution is wrong so look at whole thread ...........
That is a common definition of "e".
You can see a derivation, using a different definition here:http://www.physicsforums.com/showthread.php?t=176076