Question

Determine whether the infinite sequence converges or diverges. If it converges, find the limit.
{(1)(3)(5)...(2n-1) / (2n)^n}

Answer 1

For n > 2, you have
1*3*5/6*6*6 < 3/6^2
1*3*5*7/8*8*8*8 < 3/8^2
and so on. The nth term is less than 3/(2n)^2 so it converges to 0