已知等差数列{an}的首项为a,公差为b,且不等式ax^2-3x+2>0的解集为(-无穷,1)∪(b,+无穷)若数列{b

2个回答

  • 由ax^2-3x+2>0解集为(-∞,1)U(b,+∞)得x=1时,ax^2-3x+2=0

    a-3+2=0

    a=1

    x^2-3x+2>0

    (x-1)(x-2)>0

    x2

    b=2

    数列{an}是以1为首项,2为公差的等差数列.

    an=1+2(n-1)=2n-1

    bn=an×2ⁿ=(2n-1)×2ⁿ

    Tn=b1+b2+...+bn=1×2+3×2^2+5×2^3+...+(2n-1)×2ⁿ

    2Tn=1×2^2+3×2^3+...+(2n-3)×2ⁿ+(2n-1)×2^(n+1)

    Tn-2Tn=-Tn=2+2×2^2+2×2^3+...+2×2ⁿ-(2n-1)×2^(n+1)

    =2×(2+2^2+...+2ⁿ) -(2n-1)×2^(n+1) -2

    =2×2×(2ⁿ-1)/(2-1)-(2n-1)×2^(n+1) -2

    =(3-2n)×2^(n+1) -6

    Tn=(2n-3)×2^(n+1) +6