Question

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

Answer 1

therefore,
`((2n)!)/(n!)=(n+1)\cdot (n+2)\dots (2n)`

Explanation:

`((2n)!)/(n!)` is interesting

if we write it out for n=4

`((2n)!)/(n!)=((2(4))!)/(4!)=(8!)/(4!)=(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

`((2n)!)/(n!)=((2(3))!)/(3!)=(6!)/(3!)=(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,
`((2n)!)/(n!)=(n+1)\cdot (n+2)\dots (2n)`

there is no further information given