已知数列{an}中,a1=1,(n+1)an+1=nan,则an

题目

已知数列{an}中,a1=1,(n+1)an+1=nan,则an

答案

(n+1)a(n+1)=nan
a(n+1)/an=n/(n+1)
a(n+1)/an=n/(n+1)
.
a3/a2=2/3
a2/a1=1/2
以上等式相乘得
a(n+1)/a1=1/(n+1)
a(n+1)/a1=1/(n+1)
a(n+1)=1/(n+1)
an=1/n