Question

Determine whether the sequence converges or diverges, then compute the limit

{(2n-1)!/(2n+1)!}

Answer 1

I have never dealt with factorials before can anyone help me solve this?

Answer 2

can we use the ratio test, or is that only for series?

Answer 3

that is just for series

Answer 4

thought so...

Answer 5

just simplify and take the limit

Answer 6

\(n! = 1.2.3...n = (1.2.3.....(n-1)).n = n.(n-1)!\) This is a fundamental property of factorials. Now, the sequence that we have is \[a_{n} = \frac{(2n-1)!}{(2n+1)!}=\frac{(2n-1)!}{(2n-1)!.2n.(2n+1)} = \frac{1}{2n(2n+1)}\]
can you take it off from here?

Answer 7

ah, I see it now :0