find the limit of $\displaystyle \frac{(2n - 1)!}{(2n + 1)!}$ as n approaches infinity.
L'hop wont work b.c you cant take the derivative of a factorial. I wrote out the first three terms and they appear to be decreasing and approaching zero.
find the limit of $\displaystyle \frac{(2n - 1)!}{(2n + 1)!}$ as n approaches infinity.
L'hop wont work b.c you cant take the derivative of a factorial. I wrote out the first three terms and they appear to be decreasing and approaching zero.
$\displaystyle 0!=1$
$\displaystyle 1!=1$
$\displaystyle 2!=2\cdot 1$
$\displaystyle 3!=3\cdot 2 \cdot 1= 3 \cdot 2!$
$\displaystyle n!=n \cdot (n-1) \cdot (n-2) \cdot ... \cdot 3 \cdot 2 \cdot 1$
$\displaystyle (2n+1)!=(2n+1) \cdot (2n) \cdot (2n - 1) \cdot ... \cdot 1 = (2n+1) \cdot (2n) \cdot (2n-1)!$