# How do you write a recursive formula for the sequence 1, 2, 3/2, 4/6, 5/24...?

##### 1 Answer

Feb 23, 2016

#a_1 = 1#

#a_(n+1) = (n+1)/n^2 * a_n#

#### Explanation:

A direct formula would be:

#a_n = n/((n-1)!)#

So we find:

#a_(n+1)/a_n = ((n+1)/(n!)) -: (n/((n-1)!)) = ((n+1)(n-1)!) / (n*n!) = (n+1)/(n^2)#

Hence:

#a_(n+1) = (n+1)/n^2 * a_n#