Question

高中数学题：已知数列{an}满足a1=4/3,2-a（n+1）=12/(an+6)（n属于N*），则n∑i=1=1/ai

请问：由2-a(n+1)=12/(an+6)如何得到2/a(n+1)-6/an=1的

Answer 1

Answer 2

1、2-a(n+1)=12/(an+6)
a(n+1) = 2an/(an+6)
1/a(n+1) = (an+6)/[2an]
1/a(n+1) + 1/4 = 3(1/an + 1/4)
[1/a(n+1) + 1/4] / (1/an + 1/4) = 3
(1/an + 1/4)/ (1/a1+1/4) = 3^(n-1)
(1/an + 1/4) = 3^(n-1)
1/an = 3^(n-1) -1/4
1/a1+1/a2+..+1/an
= (3^n-1)/2 - n/4

2、bn=2/(an·a(n+1))
=(1/2)*[1/(4n-3)-1/(4n+1)]
Tn=(1/2)*[1-1/5+1/5-1/9+……+1/(4n-3)-1/(4n+1)]
=(1/2)*[1-1/(4n+1)]
=2n/(4n+1)
Tn无限接近于1/2
即m/20>=1/2【因为趋向于0.5即0.5在Tn中不可取所以可以取等】
综上m>=10
请采纳。