数列an满足：a1=1,a(n+1)=an/an +1 (1)证明1/an是等差数列.(2)数列an的通项公式

(1)
a(n+1)=a(n)/(a(n)+1)
等号两边取倒数=>1/a(n+1)=1/a(n)+1
=>1/a(n+1)-1/a(n)=1
=>1/a(n)是等差数列
(2)
1/a(n)=1/a(1)+(n-1)*d=1/1+(n-1)*1=n
=>a(n)=1/n