Finding explicit formula for recurrence relation?

Question

What would a explicit formula for this sequence? a_k = a_(k-1)/k? The way I find explicit formula is to write out some terms but this time it's not working.. I'd appreciate your help!

So, $$a_n=\frac{a_{n-r}}{\prod_{0\le k\le r-1}(n-k)}$$ DO you have any terminating condition like $a_1,a_0$ etc.? — lab bhattacharjee, Dec 20 '13 at 16:21
a_1=2. How did you get such a formula so quick? It looks complicated... — , Dec 20 '13 at 16:22
And k should be k>=2, sorry I forget to state in the problem — , Dec 20 '13 at 16:22

score 3 · Accepted Answer · answered Dec 20 '13 at 16:23

3

$$a_k=\frac{a_{k-1}}{k}=\frac{a_{k-2}}{k(k-1)}=......=\frac{a_1}{k!}$$

answered Dec 20 '13 at 16:23

Mathgrad

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Thanks! The denominator is growing so fast, must the factorial! – Dec 20 '13 at 16:27

Finding explicit formula for recurrence relation?

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