Question

16题，求过程，谢！

Answer 1

a(n+1)=nan/[n+1+(n²+n)an]
1/a(n+1)=[n+1+(n²+n)an]/(nan)=(n+1)[(1+nan)/(nan)]
1/[(n+1)a(n+1)]=1/(nan) +1
1/[(n+1)a(n+1)] -1/(nan)=1，为定值
1/(1·a1)=1/(1·½)=2
数列{1/(nan)}是以2为首项，1为公差的等差数列
1/(nan)=2+1·(n-1)=n+1
an=1/[n(n+1)]=1/n -1/(n+1)
Sn=a1+a2+...+an
=1/1- 1/2 +1/2 -1/3+...+1/n -1/(n+1)
=1- 1/(n+1)
=n/(n+1)
n/(n+1)恒>0
令n/(n+1)<2015/2017
2n<2015
n<1007.5
n为正整数，n≤1007
数列{Sn}落入区间(0，2015/2017)内的项数为1007