Prove that for any integer n ≥ 1,

(2n)!/2^n is an integer!

Well I started off saying let n=(2n!)/2^n (*)

and did the usual step like let n=1 (which is obviously true)

then when I go to let n=n+1

i get

n + (n+1) = (2(n+1))!/2^(n+1)

i can substitute the LHS n with (*)

but then I get stuck and dont know what to do

so im guessing my method is incorrect :\

can someone shed some light on this.. thanks!