(Ⅰ)∵点M在直线x=上,设M(,yM).又=, 即=(-x1,yM-y1),=(x2-,y2-yM), ∴x1+x2=1.(2分) ①当x1=时,x2=,y1+y2=f(x1)+f(x2)=-1-1=-2; ②当x1≠时,x2≠, y1+y2=+=2x1(1-2x2)+2x2(1-2x1) | (1-2x1)(1-2x2) |
=2(x1+x2)-8x1x2 | 1-2(x1+x2)+4x1x2 | ==-2; 综合①②得,y1+y2=-2.(5分) (Ⅱ)由(Ⅰ)知,当x1+x2=1时,y1+y2=-2. ∴f()+f()=-2,k=1,2,3,,n-1.(7分) n≥2时,Sn=f()+f()+f()++f(),① Sn=f()+f()+f()++f(),② ①+②得,2Sn=-2(n-1),则Sn=1-n. n=1时,S1=0满足Sn=1-n. ∴Sn=1-n.(10分) (Ⅲ)an=2Sn=21-n,Tn=1+++()n-1=2-.<⇔2(Tm-c)-(Tm+1-c) | 2(Tm+1-c) | <0⇔<0.Tm+1=2-,2Tm-Tm+1=4--2+=2-, ∴≤2-<c<2-<2,c、m为正整数, ∴c=1, 当c=1时,, ∴1<2m<3, ∴m=1.(14分) |