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

Feb 23, 2016

${a}_{1} = 1$

${a}_{n + 1} = \frac{n + 1}{n} ^ 2 \cdot {a}_{n}$

#### 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:

${a}_{n + 1} = \frac{n + 1}{n} ^ 2 \cdot {a}_{n}$