高中数列题求解

Question

麻烦写详细一些我数学不好

Answer 1

如图

Answer 2

如图

Answer 3

Answer 4

(I)
a1+a2/3+a3/5+...+an/(2n-1) = n^2-2n
n=1, a1=-1
a1+a2/3+a3/5+...+an/(2n-1) = n^2-2n (1)
a1+a2/3+a3/5+...+a(n-1)/(2n-3) = (n-1)^2-2(n-1) (2)
(1)-(2)
an/(2n-1) = 2n-1 -2
an = (2n-3)(2n-1)
ie
an = (2n-3)(2n-1)
(II)
bn
= 1/an
=(1/2)[ 1/(2n-3) -1/(2n-1) ]
Sn
=b1+b2+...+bn
=(1/2)[ 1/(2-3) -1/(2n-1) ]
=(1/2)[ -1 -1/(2n-1) ]
= -n/(2n-1)本回答被网友采纳