Question

已知数列an满足an+1/an=n+2/n(n∈正整数),且a1=1,则an=____.

麻烦懂的亲不吝赐教……

不过不要找网上的过程= =看不懂

Answer 1

a(n+1)/an=(n+2)/n
an/a(n-1) = (n+1)/(n-1)
an/a1= (n+1)n/2
an =(n+1)n/2

追问

an/a1= (n+1)n/2

这一步是怎么得到的？

追答

an/a(n-1) = (n+1)/(n-1) (1)
a(n-1)/a(n-2) = n/(n-2) (2)
...
...
a3/a2 =4/2 (n-2)
a2/a1 = 3/1 (n-1)
(1)*(2)*(3)*...*(n-1)
an/a1 = (n+1)n/2

Answer 2

题目有问题吧？将1代入也不成立啊

追问

a（n+1)/an