数列an满足a1=1/1*2=1/2,an+1/an=n/n+2 计算a1,a2,a3,a4 猜an通项 求an前n项和sn

题目

数列an满足a1=1/1*2=1/2,an+1/an=n/n+2 计算a1,a2,a3,a4 猜an通项 求an前n项和sn

答案

a2/a1=1/3
a2=1/6
a3/a2=1/2
a3=1/12
a4/a3=3/5
a4=1/20
an=1/[n(n+1)]
an=1/n-1/(n+1)
Sn=1/1-1/2+1/2-1/3+1/3+.+1/n-1/(n+1)
Sn=1-1/(n+1)