Question

已知数列an各项均为正，且a1=1,an+1an+an+1-an=0（n为正N^′） ①设bn=1

已知数列an各项均为正，且a1=1,an+1an+an+1-an=0（n为正N^′）
①设bn=1/an,求证；数列bn是等差数列
②求数列｛an/n+1｝的前n项和Sn 帮帮忙，快一点，，，，

Answer 1

(1)
a(n+1).an+a(n+1)-an=0
1/a(n+1)-1/an =1
=>{1/an}是等差数列 , d=1

1/an -1/a1=n-1
1/an = n
an =1/n
(2)
cn = an/(n+1)
= 1/n -1/(n+1)
Sn = c1+c2+...+cn
= 1- 1/(n+1)
=n/(n+1)