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#
