数列an满足a1=2an+1=2n+1an/【(n+1/2)an+1+2n】（1）bn=2n/an求bn通向（2）设cn=1/n（n+1）an+1（底n+1项

题目

数列an满足a1=2an+1=2n+1an/【(n+1/2)an+1+2n】（1）bn=2n/an求bn通向（2）设cn=1/n（n+1）an+1（底n+1项
求数列cn的前n项和sn并由此证明5/16≤sn＜1/2

答案

（(n+1)^2+1]/n(n+1)=(n²+2n+2)/(n²+n)=1+(n+2)/(n²+n)=1+1/(n-1+2/(n+2))=1+1/((n+2)+2/(n+2)-3)(n+2)+2/(n+2)是个对钩函数,最低点是(n+2）=2/(n+2)此时n解出来小于0所以(n+2)+2/(n+2)是个单调递增...