Question

已知函数f(x)=(7x+5)/(x+1),数列an中,2an+1-2an+an+1an=0,a1=1,且an≠0,数列

Answer 1

(1)

2a(n+1)-2an+a(n+1)an=0

1/a(n+1)-1/an= 1/2

{1/an}是等差数列, d=1/2

(2)

1/an -1/a1= (n-1)/2

an = 2/(n+1)

bn=f(an -1)

= f((1-n)/(1+n))

= (7[(1-n)/(1+n)]+5)/([(1-n)/(1+n)]+1)

= (12-2n)/2

=6-n

(3)

bn > 0

n< 6

for n>=6

|b1|+b2|+...+|bn| = (11-n)n/2

for n >7

|b1|+b2|+...+|bn|

=(b1+b2+...+b6) -(b7+b8+...+bn)

=15 + (n-7)(n-6)/2