数列{an}中,a1=2,a(n+1)=an(n+1)/n,求{an}通项式

数列{an}中,a1=2,a(n+1)=an(n+1)/n,求{an}通项式

a(n+1)/a(n)=(n+1)/n
a(n)/a(n-1)=n/(n-1)
.
a2/a1=2/1
依次相乘
an=n*a1=2n

an=a(n-1) n/n-1
a(n-1)=a(n-2) n-1/n-2....
a2=a1 2/1
左边相乘等于右边相乘，得an=na1=2n