s(n)/n=n,s(n)=n^2,
a(1)=s(1)=1,
a(n+1)=s(n+1)-s(n)=(n+1)^2-n^2=2n+1=2(n+1)-1,
a(n)=2n-1.
b(n)=1/[a(n)a(n+1)] = 1/[(2n-1)(2n+1)] = (1/2)[1/(2n-1) - 1/(2n+1)],
t(n)=b(1)+b(2)+...+b(n-1)+b(n)
=(1/2)[1/1-1/3+1/3-1/5+...+1/(2n-3)-1/(2n-1)+1/(2n-1)-1/(2n+1)]
=(1/2)[1/1 - 1/(2n+1)]
=n/(2n+1)
(-1)^n *m < 2t(n) = 2n/(2n+1)
n 为奇数时,-m < 2n/(2n+1),m>-2n/(2n+1)=1/(2n+1) - 1,m>1/(2*1+1) - 1 = -2/3.
n为偶数时,m < 2n/(2n+1) = 1-1/(2n+1),m