2)数列{ an }中,a1=1,an+1= 2an/an+2求an通项公式.(其中n,n+1为下脚标)
问题描述:
2)数列{ an }中,a1=1,an+1= 2an/an+2求an通项公式.(其中n,n+1为下脚标)
答
a(n+1)=2an/(an + 2)
1/a(n+1)= (an + 2)/2an = 1/2 + 1/an
1/a(n+1) - 1/an = 1/2 所以1/an 为等差数列,公差是1/2
1/an = 1/1 + 1*(n-1)/2 = (n+1)/2
an = 2/(n+1)