1. The problem statement, all variables and given/known data
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges find its limit.
an = (1*3*5*....*(2n-1))/(2n)n
2. Relevant equations
lim n->infinity an = L
3. The attempt at a solution
The answer in the book shows:
1/2n * 3/2n * 5/2n....(2n-1)/2n less than 1/2n
So, lim n->infinity an = 0, converges
I don't understand where the 1/2n * 3/2n * 5/2n....(2n-1)/2n less than 1/2n comes from. I'm obviously missing something. Could anyone please explain that part to me? I'd really appreciate any help at all. Thanks :)
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges find its limit.
an = (1*3*5*....*(2n-1))/(2n)n
2. Relevant equations
lim n->infinity an = L
3. The attempt at a solution
The answer in the book shows:
1/2n * 3/2n * 5/2n....(2n-1)/2n less than 1/2n
So, lim n->infinity an = 0, converges
I don't understand where the 1/2n * 3/2n * 5/2n....(2n-1)/2n less than 1/2n comes from. I'm obviously missing something. Could anyone please explain that part to me? I'd really appreciate any help at all. Thanks :)
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