叠加,叠乘(1713:32:17)a1=3,nan=(n+2)an-1(n≥2）,求an

Question

叠加,叠乘 (17 13:32:17)
a1=3,nan=(n+2)an-1(n≥2）,求an

Answer 1

n>=2时,an/an-1 =(n+2)/n
a2/a1=4/2
a3/a2=5/3
a4/a3=6/4
a5/a4=7/5
a6/a5=8/6
.
an/an-1=(n+2)/n
两边相乘并约分得：
an/a1=(n+1)(n+2)/6
所以 an=(n+1)(n+2)/2
又n=1符合上式,
所以 an=(n+1)(n+2)/2