数列an,a1=1.an+1/an=n+2/n,求通项公式,

Question

数列an,a1=1.an+1/an=n+2/n,求通项公式,

Answer 1

因为a1=1,a(n+1)/an=(n+2)/n
所以 an=(n+1)/(n-1)*a(n-1)=(n+1)/(n-1)*n/(n-2)*a(n-2)=.
=(n+1)/(n-1)*n/(n-2)*.*4/2*3/1*a1
=(n+1)n/(2*1)*1
=n(n+1)/2