(1) a2=-1/8,a3=1/24
(2)a2-a1=1-1/2
a3-a2=1/2-1/3
a4-a3=1/3-1/4
......
an-an-1=1/(n-1)-1/n
累加得 an-a1=1-1/n
an=3/8-1/n
(3)bn=n(n+1)/2*(3n-1/8n)
= (3n-1)(n+1)/4
=3/4×(n^2+2/3n-1/3)
=3/4*[(n+1/3)^2-4/9]
所以 bn在(1,+∞)上递增
bn min=b1=-5/8
(1) a2=-1/8,a3=1/24
(2)a2-a1=1-1/2
a3-a2=1/2-1/3
a4-a3=1/3-1/4
......
an-an-1=1/(n-1)-1/n
累加得 an-a1=1-1/n
an=3/8-1/n
(3)bn=n(n+1)/2*(3n-1/8n)
= (3n-1)(n+1)/4
=3/4×(n^2+2/3n-1/3)
=3/4*[(n+1/3)^2-4/9]
所以 bn在(1,+∞)上递增
bn min=b1=-5/8