Consider the ratios between adjacent terms of the given sequence:

`1/2 : 1 = 1/2,` `1/6 : 1/2 = 1/3,` `1/24 : 1/6 = 1/4,` `1/120 : 1/24 = 1/5.`

We see that the `n` -th term of the sequence may be obtained from the `(n-1)`-th term by multiplying by...

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Consider the ratios between adjacent terms of the given sequence:

`1/2 : 1 = 1/2,` `1/6 : 1/2 = 1/3,` `1/24 : 1/6 = 1/4,` `1/120 : 1/24 = 1/5.`

We see that the `n` -th term of the sequence may be obtained from the `(n-1)`-th term by multiplying by `1/n.`

Therefore the `n`-th term may be predicted to be equal to

`a_n = 1/(n(n-1)(n-2)...) = 1/(n!)`