Question

已经知道数列{an}中,a1=1，an+1=2an/an+2求证数列{1/an}是等差数列

Answer 1

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
}是以1为首项1/2为公差的等差数列，
1/an
=
1/1
+
1*(n-1)/2
=
(n+1)/2
an
=
2/(n+1)

Answer 2

a1=1
a（n+1)=2(an)/a(n+2)
1/a（n+1）=（n+2）=1/2+1/an
1/a（n+1）=1/an+1/2又1/a1=1
《1/an》是以1为首项1/2为公差的
等差数列

Answer 3

a(n+1)=2an/3an+2=1/(3/2+1/an)
1/a(n+1)=3/2+1/an
1/a(n+1)-1/an=3/2
1/a1=1
d=3/2
an>0
{1/an}是等差数列

Answer 4

等式两边分子分母颠倒
左边成为1/an+1=（an+2）/2an
=
1/2+1/an
化成等差的规定式
没啦