数列{an}与{bn},an=(1/2)n^2-7n+18,bn=2+(1/2)^(n-3),是否存在K属于正整数,使ak-bk属于（0,1/2）?
问题描述：
数列{an}与{bn},an=(1/2)n^2-7n+18,bn=2+(1/2)^(n-3),是否存在K属于正整数,使ak-bk属于（0,1/2）?
答
an-bn=(1/2)n^2-7n+18-2-(1/2)^(n-3)=(1/2)n^2-(1/2)^(n-3)-7n+16n=1或n=2,n=3时an-bn>1n>3时,1>(1/2)^(n-3)>0(1/2)n^2-7n+16 >an-bn>(1/2)n^2-1-7n+16(1/2)(n-7)^2-17/2>an-bn>(1/2)(n-7)^2-19/2n=11(-1/2)>an-bn>(...