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
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!