An = (2n-3)/(2n+1) × a (n-1), then: an/[a (n-1)] = (2n-3)/(2n+1).
a2/a 1= 1/5
a3/a2=3/7
a4/a3=5/9
a5/a4=7/ 1 1
……
an/a(n- 1)=[2n-3]/[2n+ 1]
Multiply all the above formulas to get:
An/a1= 3/[(2n-1) (2n+1)], substituting a 1= 1/3, with: an= 1/[4n? - 1]