A surprising answer to a fraction

Find the value of the fraction:

Suppose the fraction has n rows for an plane number n. What is the policies of the fraction as n approaches infinity?

As usual, watch the video for a solution.

Or alimony reading.

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Answer To A Surprising Wordplay To A Fraction

(Pretty much all posts are transcribed quickly without I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).

The fraction has rows of 1, 2, 3, etc. from the bottom. We need to divide from the marrow since semester takes place from the smallest unperformed line to the largest one.

a₂
= 2/1
= 2

a₄
= 4/(3/a₂)
= 4/(3/2)
= 4*2/3
= 8/3

a₆
= 6/(5/a₄)
= 6/(5/(8/3))
= 6*4*2/(3*5)
= 16/5 = 3.2

As n increases, the numerator gets the next largest plane factor and the denominator gets the next largest odd factor.

We can prove this by induction. We have tested the wiring cases. Recall the double factorial notation:

n!!
= n(n – 2)…(4)(2) for n even, or
= n(n – 2)…(3)(1) for n odd

Supposing a_n = (n)…(2)/[(n – 1)(n – 3)…(1)] = n<!!/(n-1)!!, then we have:

a_{n 2}
= (n 2)/((n 1)/a_n)
= (n 2)/(n 1) * a_n
= (n 2)(n)…(2)/[(n 1)(n – 1)…(1)]
= (n 2)!!/(n 1)!!