Question

Find the value of the following (2n)!/n!​

Answer 1

Answer:

therefore, $\frac{(2n)!}{n!}=(n+1)\cdot (n+2)\dots (2n)$

Step-by-step explanation:

$\frac{(2n)!}{n!}$ is interesting

if we write it out for n=4

$\frac{(2n)!}{n!}=\frac{(2(4))!}{4!}=\frac{8!}{4!}=\frac{1\cdot 2\cdot 3\cdot 4\cdot 5 \cdot 6\cdot 7\cdot 8}{1\cdot 2\cdot 3\cdot 4}=5\cdot 6\cdot 7\cdot 8$

try for n=3

$\frac{(2n)!}{n!}=\frac{(2(3))!}{3!}=\frac{6!}{3!}=\frac{1\cdot 2\cdot 3\cdot 4\cdot 5 \cdot 6}{1\cdot 2\cdot 3}=4\cdot 5\cdot 6$

we notice that the first $n$ terms cancel out

therefore, $\frac{(2n)!}{n!}=(n+1)\cdot (n+2)\dots (2n)$

there is no further information given