n-1-x-a-n-9-x-a-4-

Question Number 12326 by sin (x) last updated on 19/Apr/17

\underset{n = 1}{\prod^{x}} a_{n} = 9^{x!}

a_{4} = ?

Answered by nume1114 last updated on 19/Apr/17

a_{x} = \frac{a_{1} \times a_{2} \times \dots \times a_{x - 1} \times a_{x}}{a_{1} \times a_{2} \times \dots \times a_{x - 1}}

= \frac{\underset{n = 1}{\prod^{x}} a_{n}}{\underset{n = 1}{\prod^{x - 1}} a_{n}} = \frac{9^{x!}}{9^{(x - 1)!}} = 9^{x! - (x - 1)!}

a_{4} = 9^{4! - (4 - 1)!} = 9^{24 - 6} = 9^{18}

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