Question

Show that the quantity (n+1)(n+ 2)... (2n-1)(2n) is divisible by 2^n​

Answer 1

You can also proceed by induction.

Let an=(n+1)(n+2)…(2n).

Then an+1/an=(2n+1)(2n+2)/(n+1)=2(2n+1).

Since 2n+1 is odd, only one 2 factor is added at each step.

Since a1=21, you get an=2n×on where on is an odd number